I will take some photos and post. Our yard is a mess after returning from our trip, but we are slowly trying to get it back in shape! It's also tiny, but it might give you some ideas.
Your yard is going to be awesome!
We have a TON of rabbits, squirrels, and chipmunks. They eat our blueberries and tomatoes, but seem to leave the kale, swiss chard, herbs, and non-tender greens alone. My husband built some beautiful miter-edged garden boxes and set them on top of Belgian block. The total height is probably 15" or so. The rabbits don't bother jumping in (they go after the roses, hosta, and coneflower instead), but the squirrels get in and go for the tomatoes. We might end up draping the tomatoes with mesh and see if that helps. A local farmer told me that aluminum pie plates on wooden stakes is how they keep animals out of their beds.
If you don't like herb containers, I would plant some herbs around the base of the tree in your backyard. I would do it in a circle to break up the squares and rectangles elsewhere and edge it nicely with an edging tool. Or plant a boxwood hedge in a circle. I don't think small animals are likely to bother your herbs too much. Another nice idea for that tree would be a wildflower copse. Your kids would love the butterflies and bees, and would give you a constant supply of fresh cut flowers. Or hang a simple, sweet rope swing from the tree with no plantings underneath?
I thought of bean teepees because kids like to go inside them. You could put a few tree stumps inside for the kids to sit on. We are training a weeping cherry to have enough room for tree stumps underneath. It's very cute.
I think it would be really pretty to add some lavender or Russian sage to flank the entrance to your raised bed area to "invite" you into the space. Like creating "rooms" in your yard.
Obviously, I like pretty more than function!!! I'm sure you'll get better, functional advice from the other ladies!!!!! 
Follow Mothering