I've always heard that weed and feed should only be used in the cooler months. If you apply it now it will kill your grass. Sorry.

15-0-0 is the fertilizer analysis. You will see 3 numbers in that format on most every fertilizer that exists. The first number is the percent of product by weight that is Nitrogen, the second number is Phosphorous and the third Potassium (sometimes called Potash). For lawn fertilizer all you need is Nitrogen. Phosphorous has a potential to leach into water sources and contaminate streams, so it should only be used when you actually need it to get results. Potash isn't bad for anything, but it also doesn't do your lawn much good, and over-applying encourages dandelions. As to Weed and Feed, it contains some Nitrogen, which will make your grass grow in thicker and greener, and also 2-4D. 2-4D is one of the most common herbicides in the world, it specializes in exterminating broadleaf weeds (dandelions, clovers, etc.) without harming grasses. Applied even close to to directions, it should remove most lawn weeds without harming your grass. Be careful when you get close to any flower beds or vegetable gardens though, it has a potential for going a little past where you were aiming, and some species of plants (especially vines and melons) respond VERY poorly to 2-4D. I wouldn't call it 'totally safe' for people, but as herbicides go it's pretty safe. Give it time enough to dry on and soak in, then you're fine.

This one should work. Safe for floratam. Hose end sprayer. http://www.ortho.com/smg/goprod/ortho-weed-b-gon-weed-killer/prod11360002?locale=en_US More expensive that is also safe for floratam. Out of stock here but available elsewhere. http://www.domyownpestcontrol.com/celsius-wg-herbicide-p-1923.html Don't worry about the mediocre reviews for the Ortho product. Most folks don't bother to read the label and then misapply. I've used Weed B Gon products with great success. It's more about the ingredients than the brand and proper application.

I use Milorganite in the spring as well, for summer and fall I use the Scott's Turfbuilder product designed for that season. I am by no means a lawn expert though, these are just easy to find, relatively inexpensive products that do the job well enough for me. I'm confident you could kill the ivy (and not your trees) if you have the time and patience. Again I'd suggest trying the Weed B Gon Chickweed Clover & Oxalis concentrate in an Ortho Dial N' Spray hose end sprayer. Just pick a calm day and get down low to avoid spraying the tree trunks and leaves. If the ivy is anything like wild violet it will take a couple of applications but it will work eventually. Then like you mentioned you'll have to rake out the dead ivy and reseed the bare patches. But as others have said, a weed-free (or even weed sparse) lawn is a huge commitment so I don't blame you for hiring it out--if you can find someone to call you back. Last thing I'll say is that no matter how diligent you are about your own lawn, if your neighbors aren't equally diligent you will always have some of their dandelions, clover, ivy, etc. filtering into your lawn. So I've lowered my expectations and live with a semi-weed free lawn after 13+ years at my current house.