show signs of depression when the bunnies leave her and go to their new homes? Also, if I keep a doe out of the liter, would it stay bonded to the mother to share a hutch?
Some mother/daughter pairs can bond. Others won't. Depends on the individual rabbits. Having them both spayed will increase the likelihood of a bond, but isn't a guarantee.
In our experience most does seem relieved when the litter of kits are gone. There may be the occasional doe who misses them, but rabbits generally don’t share emotions same as humans.