I don't think
Ambrose is too formal for a kid. One of my students this year's younger brother is named
Ambrose (sibset:
Gerard (10) and
Ambrose (8)). I feel like it's one of those names that seems too formal, but works out just fine.
I don't know that I have any good nickname suggestions. I'd probably stay away from Rose/Rosie or
Amber. Maybe Amb? Amby? Brose?