Welcome Charlene! Your garden sounds so nice. And your pickles are fine, but I'll go point-by-point to make sure I hit all the important stuff.

"-We ran them through the dishwasher"
Good, you need clean jars, and they are less likely to break if they are hot when you pour in the brine.
"-We brought to a low boil simmer:"
Fine. You can also find brines that have some water to make the pickles less tart, but you want to use a tested recipe that is at least 50% vinegar. I would skip the alum. It's a form of aluminum, which is not great to ingest. Next time you can use Pickle Crisp, which is calcium chloride powder to add to each jar; it's sold at Walmart near the canning jars. But alum would not stop me from eating this batch of pickles.
"we did not use tongs or anything just used our hands."
I always pack jars with clean hands.
"BUT we ran out of the vinegar solution"
As long as the recipe didn't say to boil the brine for x minutes before using, you are fine. You did right using the same ingredients. The only danger in waiting to fill the last two jars is if they get cold, the hot brine may cause thermal shock & break the jars, which obviously didn't happen.
"-We put the cap w/rubber seal and screwed the tops on tight from the dishwasher"
This is ok for fridge pickles. When you can in a boiling water bath, you will want to put the tops on "fingertip tight," in other words using your fingertips & turning just until you meet resistance. This leaves room for the air to expand out of the jar, which creates a vacuum seal upon cooling.
"-Let them sit out for two hours to room temperature"
This is ok too. Normally you want to get food cold asap to avoid bacterial growth, but for pickles it's probably not a huge deal. If you do put them straight in the fridge, you should go for rack-bottom shelf, not a flat glass shelf which will speed heat transfer from the bottom & possibly cause breakage (brine in the fridge is a nightmare, I can tell you that from personal experience). You are right that fridge pickle jars do not seal. They will be crisper than pickles that have been heated in a boiling water bath.

So, the things I would change for next time are the alum and the time between filling & refrigerating. Also, I prefer to use a tested recipe from the Ball Blue Book, from the USDA, or from a forum member who gives the recipe's credentials.

About the two months...I sometimes keep things way longer than I'm supposed to. Pickles are one of the safest products to can as long as you use enough vinegar, which you did. Personally I wouldn't choose to give them away after the "expiration date," but I would keep eating them until they were finished, or until they showed signs of spoilage like unusually soft or slimy pickles, mold floating in jars, bad smell.

Open kettle canning is when you start out like you did, but then you put the jars on the shelf instead of in the fridge. It is no longer recommended by the USDA for any products. There are people who still do it, but I think it's best not to do it unless a person has a lot of experience and can really predict how that will affect the food (e.g., for jam, you will notice if it gets moldy, but other foods may be more sneaky about spoiling).

A few other notes about pickles: as long as you have 50% vinegar, you can add whatever spices you like (but adding 1/4 cup of dill might count as another vegetable instead of a spice!). Other vegetables may need more vinegar, e.g. garlic must be pickled in 100% vinegar. Some recipes can be processed for longer times at 180F to try to make them less soft than boiling (known as low-temperature pasteurization), but make sure the recipe is approved for this method.

Here is a link to a discussion of pickles that has a few different recipes and a discussion of fridge pickles. Enjoy your pickles and the time with your son!

Melissa

Just to add to what Melissa said, you have far more latitude with a refrigerator pickle than with one that's going to be sitting on a shelf. So she's right; you have nothing to worry about.

The pickles will also be good far longer than the recommended time, probably as long as it takes you to consume them. However, over time they will soften, so the texture may be less pleasing.

Many Extension services still say it's OK to use alum in limited amounts but they no longer recommend it or provide recipes using it because it's been supplanted by the Pickle Crisp-type products. Some object to alum because it's an aluminum, though in miniscule amounts considering most of us don't live on a diet of pickles. If too much alum is consumed (I've never known it to happen.) it can cause stomach upsets. So don't consume those wonderful pickles more than a quart at a time!

Carol

The alum will not work in a quick pack or refrigerator pickle, and it will acutally make them softer over time. In a fridge pickle, you don't need Pickle Crisp, either.
The only time alum will help is when fermenting pickles.
Other than that, your refrigerator pickles are fine.

Now, this is for quick pack pickles, ones you make and process, not refrigerator pickles.... You get concerned about botulism in pickles if a person uses an old outdated recipe that doesn't have enough vinegar to safely preserve them. Cucumbers are low acid veggies, it takes at least half of the brine to contain 5% acidity vinegar to water ratio to make them acidic enough to process and keep on the shelf. Many old recipes were based upon vinegar that was up to 40% acidity vinegar. Then, quick pack pickles are processed to destroy bacteria in and on the jars, and to create a true vacuum seal, not a surface seal. This is some basic pickle safety info to help you.

I would only keep the fridge pickles for the recommended time, though, since bacteria is present WAY before you see any signs of spoilage.

"My 9 yr old son and I have really found something we can do together and he is thriving on the growing, picking, and eating (some of it-still doesn't like some of the vegetables). He wakes up every day and runs to the garden first thing checking it several times a day."

This is something I love to hear. Your son will get a lifetime of pleasure from this.

Jim

Linda Lou provided valuable information regarding the uselessness of alum in a non-fermented pickle and the importance of vinegar/water ratio in a canned product.

However, as you research you will find variations in information from equally reliable sources. Below I've posted a good example of how even Extension services will differ in their recommendations.

Carol

Thanks so much for all the info! I feel like I've been to a pickle education course.

So, I guess I didn't do toooo bad for my first time. But it seems my recipe from the internet was a little dated. Will be more discerning about where my recipes come from next time.

When I bought the alum, which I'd never heard of before, it said on the back that it was made from watermelon so I figured it was okay. But I mostly do pesticide/chemical free as much as possible and this is why I didn't choose the dill mix packets they were selling at Walmart. Oh well, I'll do different next time :)

Today we made jelly from our grapes with my neighbor. I jumped up and down and squealed when I heard the first few "pings".

I feel like Laura Ingalls (my favorite show!), so self sufficient, granola-head, Martha Stewart, earth-mama, etc. :) :) :)

I normally post on the Rocky Mountain Gardening (RMG) forum, but I'm sure I'll be back. I got a rather large crop of habaneros that are way too hot for us so I thought I'd try the Habanero Gold recipe I saw on here.

Thanks again for the kind words about my son too :)
Charlene

I've put a link up of the new veggie garden if you're interested. We have big plans for it next year....

Charlene, welcome to the forum! Those are some nice grapes you have going there, I haven't gotten my young Concords to bear yet.

I'm way too late to help you on pickles, and I'm not much good at pickles anyway. Now, if you decide to make that Habanero Gold, I can help you on that!

I love to have my kids, and now my grandkids, garden with me. My great-niece and great-nephews garden with me too, growing things for the County fair. It's a great way to spend time with them.

Happy Canning.

Annie

I don't think your recipe sounds dated. Dated recipes are ones that seal jars without a boiling water bath or a pressure canner, like open kettle canning or the inversion method. These are unsealed, refrigerated jars, so I wouldn't even consider this to be "canning".

As readinglady's link says, spoilage of these pickles should be obvious (have you EVER had an open jar of pickles in the fridge go bad?). You needn't worry about botulism with refrigerator pickles, just the kinds of things that make fresh vegetables moldy or slimy or smelly.

For refrigerator pickles, I like to use the Ball plastic twist-on caps. They're less hassle than the two-piece lids, they don't rust, and they don't react with the vinegar. They also help remind people I might give the pickles to that they aren't canned and must be refrigerated.