Tree peony is grafted on herbaceous peony. sometimes rooted peony grows.
Rule of thumb: you are not supposed to let the herbaceous grow. If you let it grow, tree peony may not survive.

If you plant together, you don't know which one is growing(root plant or the one you planted).

Not only that, tree peony grows big over the years herbaceous may not do good under it.

I am not expert. I am beginner too. These 2 points strike in my mind when I read your post.

It would be helpful to know where your mother lives, what part of the country. For most areas I would keep four feet apart and plant in the full sun. For some locations full sun may be too much for the tree peony. Al

Thanks Calistoga. She lives in Central Kansas. Four ft. sounds about right!

Like the others said, you will probably want to keep them separate, but there's nothing wrong with planting other flowers nearby to give it the look that you had wanted -- a mix of two kinds of flowers, one staged to be shorter than the other.