Your dogs look like they might do a good job of keeping critters out of your yard!
All trees will drop some branches and leaves, that just goes with the territory. If you're really that afraid of trees, build an awning over your deck for shade. There are comapanies that will custom install awnings for you.
That said, a good tree for shade is red maple, they sell special varieties in the stores that are bred to grow fast. Another shade tree people like around here because their leaves are small so don't need a lot of raking, is honey locust. That's the tree you see in a lot of parking islands, so pretty trouble free. I think there is even a variety called "Shademaster."
A tree I like is japanese red maple. Lots of people grow those. They are kinda pricey, but I got mine from a mail order source for not too much. But make sure to get a variety that gets big, some dwarf varieties will be small. "Bloodgood" is a common red-leaves variety.
Another shade option are those big tent like things they are selling in all the big box stores. Some folks around here have them on their decks and they don't look too bad. Also they make pretty big patio umbrellas nowdays, some almost as large as a small tree.

Thanks! The dogs do good, even caught a wild box turtle because my dogs were barking at it in my yard. Showed my kids and husband when they got home, then set it free again in the woods.
I am not scared of the smaller branches trees drop, but we get some scary thunderstorms out here, and always hearing about tree branches falling off and killing the family inside the house. About 2 months ago this happened not to far from my house, killed a daddy and his 2 year old son in bed. So sad.

The honey locust, I heard they have sharp thorns? Do you know of any that don't? I also love red maples. Time to hit google.

Anyone one else have any ideas how to make this visually appealing, but functional for kids and pups?

Black locust is the tree with the biggest thorns, not honey locust. But common names can be misleading, since both trees have the name "locust" and both wild varieties have thorns. The specific tree I mentioned, with the scientific name Gleditsia tricanthos, has varieties that have been bred to be thornless. I believe the most commonly available variety is "Shademaster."

Here is a link that might be useful: Thornless honey locust

I think that whatever you plant may need enclosure to protect it while young. This could be something on stakes like a tomato cage only maybe sturdier.

I would tend to visit your local nurseries and look for small, growing trees, but really the trick to not being killed by your trees is to not let them get too big. If you get something fast growing, just plan to cut it down after 10-15 years and replace it, a slower-growing variety maybe less often. If you have maybe four tree-planting spots, you can plant them on a rotating schedule so you aren't going from all or nothing to the other extreme all the time. You just replace one tree every five years or so.

Other than this I wonder if a specimen shrub arrangement would work for you. It would lose your kids a soccer pitch, but it would be fun for other uses, and would give shady places without providing cover for critters. Pick maybe five nice and vigorous shrubs, things like hibiscus or mock orange or elderberry or vitex or ninebark or whatever works in your area (isn't Franklinia native for you??) and plant them, with protection and something that allows you to mow around them, just "somewhere" in the yard, individually as specimens. When those shrubs grow you might be surprised at how much shade tall shrubs can provide. Don't buy anything that spreads by suckers though - at all costs, avoid flowering quince!

In your planters, again it's all about you being more determined than the dogs. But some things just won't work out (that is, they'll win) and then it's just best to let it be a dog spot. I wouldn't do a lot of foundation planting in the back yard in any case. Also, I think dogs prefer unpaved runs.

KarinL

Thank you for the useful info!