I believe you are wanting to make a "reversible quilt", that is the top and backing are both pretty.

No, quilt backings do not have to be "simple".

Yes, do it. Just treat it as a backing. I have made quilts that are reversable.

Awesome!!! Thanks ladies. Would it be more visually appealing to have the same pattern on both sides or change it up?

Keep in mind it will be thick. You will have double the seams to quilt through so you'll need to try and not let seams lay in same spots on both sides and quilt it with something simple like straight lines using feed dogs up. It will be bulkier but a real treasure if you can do it.

Thanks toolgranny. That's something I didn't think about.

If it gets too thick, use a thinner batting or use flannel as the batting, just be sure to wash it a couple of times with hot water and dry with high heat. Flannel shrinks like crazy so do it before you use as batting. Or if you have a lot of the clothes, why not just make 2 quilts? Your post did indicate kidS as in multiple :)
just a thought

I would indeed make more than one quilt.

I usually do a pieced back because I like to use up my fabric. Fabric is so expensive, and it seems so practical and interesting to use it that way. I made a quilt for a great niece of mine, and I arranged the pieces in the back to be a giant purple checker board. She and her sister tell me they love to play checkers in her room on it.