Thanks for the reply Roy!

Yes, I have heard about the root invasion problem with Beech tree, but
one thing that I did not mention was that when the old Red Bud was
mature, I put down a circle of purple colored bricks around its'
perimeter... about 8 feet (3 meters) in a diameter circle.

I have also considered a 'ThunderCloud' Plum and a 'Forest Pansy' Red
Bud. I think the Forest Pansy will COOK in the sun of my front yard, and
both trees are a little to dark (foliage) for my taste.

Do you think that the Tri-Color will have a problem with the bricks...
or will the bricks help with the root control (somewhat)?

Also, do you think that cutting-off the leader (main branch) might help?
I've heard that this tree will reach 50 feet tall (17 meters) when
mature.