It's going to take a while for a shade tree to get big enough to shade out a garden. You'll have quite a few years in which you can plant sun loving veggies, the veggies that do better with a little shade, like lettuce and spinach. As the tree gets bigger, you can transition to growing things like raspberries and hostas (the shoots supposedly taste like asperagus), wild strawberries, blackberries, violets/pansies (edible), fushias (flowers are edible), rhubarb, chives, elderberry, thimbleberries, huckleberries, miners lettuce, nettles, etc.
When the tree gets really big, you can trim out the lower branches to allow sun under the tree, while still shading the top of the house. If you plant a maple, you could even probably tap it for sap!
Looking at the areal picture, I really don't see why you can't have both a shade garden and a vegetable garden a little further out. You have big front yard, and the sun goes across the sky, so a lot of area will get hours of morning or evening sun. I did a little photoshop mock-up with a cut and pasted tree where you'd probably want it for day and evening shade. I also did extremely loose depictions of where your full sun, part sun, and shade would be in like, 10-20 years when the tree is huge (hard to tell exactly because the amount of light changes during the year and I can't tell exactly where all the other trees are or how tall they are/will be). But, you can see that even with a huge tree, you'd still have a lot of area to grow veggies and other edibles...and in the 10-20 years leading up to that, you'll have even more growing area.
I have a lot of shade on my sloped, north facing property, and I still manage to grow lots of veggies and fruit. I grow my veggies in the few areas that get lots of sun, and grow my fruit trees in the areas with a little less sun, and my berries in the shadier spots, and the shadiest spots often are my "zone 4" and "zone 5" areas where I let things be a little more wild for habit. There's only so many hours in the day, so I'm happy to let some areas slide. I've got a three year old and a 9 month old, so I totally understand not having time to manage a garden! I really should start a thread on how to garden with wee ones, because we all need tips and tricks for keeping them busy. But, I did find some other threads that might help with the making-time-to-garden-with-young-children thing (
https://permies.com/t/54338/Children-gardening,
https://permies.com/t/50429,
https://permies.com/t/52261/time-growing-family-starting-homestead). Don't be afraid to start small and only grow a little--life is crazy at this stage and it's okay to only do a little if that's all you have time for!
Wow, this was long! I hope something in there helps!