It is much better to grade away from the building for several feet (10') so that water drains away from it, rather than catch water at the building and put it in a pipe to be carried away. Seems like a gentle gradual swale would be useful for you along the side of the house to collect water and direct it toward the back yard.

A french drain in my mind is a hole in the ground, often filled with stone and covered with soil that acts as temporary storage "container" for a finite capacity of water, which slowly seeps out of the hole and into the ground. Placing a french drain like that near the house would invite additional storm water to soak into the ground close to the foundation. Such drains are easily overwhelmed in large storms so it's better to use proper grading. While you would need to determine depth of utility lines, it's not likely they're so shallow that they would affect proper grading. At any rate, they may be able to be adjusted, if necessary.

A potential avenue to research would be the installation of a strategically placed rain garden or two. You can install catch basins below your gutter downspouts and pipe them directly into your rain garden. Besides helping with your water issue there are many other benefits to creating a rain garden. For example: Rain and melting snow (if you live in MN like myself) runs off your roof, driveway and even your lawn, directly flowing to the street and inevitably down the storm drains. All of this runoff, when untreated, carries pollutants like oil, salt, fertilizer and pesticides that are being directed right into our rivers, lakes and streams. This is causing major issues with our fresh water! Your rain garden(s) will capture all that runoff and hold thousands of gallons of rainwater that can be used to feed your beautiful garden and surrounding plants while also infiltrating water deep into the ground helping to maintain your water table. Plants, mulch and soil effectively break up the pollutants and make them non harmful to us. Lastly, a rain garden is not only beautiful, it creates a habitat for birds and beneficial insects and not to mention it makes a great statement for your appreciation of nature and humanity,

Thank you both for the reply and help. Sorry I am just now responding to this. I couldn't find my post and I just figured out how to search for it. :)

If I would do a swale, I'm guessing I would need to find someone with a bobcat? I was wanting to do this myself to save on cost, but I would be doing it with a shovel.

How far out should the swale go to? Do I need to tear out the three trees?

Thanks for the help again!!!

I don't think you need to tear out any planting, You might end up needing to grade by hand immediately around the trees if soil needs to be lowered around them (which would end up looking like the trees were on little hills. We're talking very few inches here.) Other than that develop a shallow swale a distance away from the house that intercepts all of the water running off of the hill toward the house. Not sure this sketch will be helpful; just trying to give you the general idea.

Yardvaark, that does help a lot! Thank you!

Is there a certain depth that the swale needs to be?

The volume of water is a complex computation about which I know zero facts. If I was doing this in my yard, I'd make a "gut" estimation about the size of the "river" that could possibly flow through this space in a very heavy storm. Then I'd factor in about 50% greater holding capacity for the swale, figuring that I want to accommodate what I think will run though this area, plus more, just in case. Keep in mind that the wider the swale is, the shallower it can be. You don't want to make a trench that is difficult to mow. You want a nearly imperceptible swale that is easy to mow and easy to traverse. It should be well blended into the surrounding areas.