The batting will hold up, but quilting 10" apart will put a ton of stress on the thread & fabric for a utility quilt. Children's quilts generally should be quilted 2" or LESS apart to provide enough sturdiness for regular washing & heavy use. 10" apart with cotton thread will last generally for about 2 years if laundered regularly before issues with the thread or fabric can start to crop up; because mono doesn't swell like cotton thread, as the needle holes start to wear, mono thread will not fill that space in like cotton. Cotton thread is easier to work with for new beginners than mono & will hold up a bit better in the wash.
I would pick a 50wt/ 2ply (or 60/3) cotton thread that matches the top & not worry about the back. 50/2 is very thin & really will not show up. Working with a Walking Foot is pretty easy to learn; it's not like learning to FMQ. If you still really want to use mono, I'd do mono only on the top & a matching 50/2 cotton in the bobbin.
Once you've done a couple of pieces with cotton thread, I do believe there are some rare instances where mono is the best choice. That said, after seeing for over 20 years, I STID'ed my first quilt, using mono because I thought that was the best choice for newbies. It was a nightmare to work with & after maybe a dozen or so trips through the wash, the stitches started snapping in probably 8 places & I've had to re-quilt the whole table runner. That is not a flaw of mono thread -- it's a problem that happens when inexperienced quilters try to work with one of THE most finicky threads out there without making the many accommodations needed to successfully quilt with mono.