Hi, I've had various cats, but never quite your situation. However, chances are that the mother raised her kittens indoors, in the proximity of a litter-box, given that she is in such good shape, and (I assume) so friendly to people. If not, if she has been trained to properly bury her business by her mother, she may take to the litter-box anyway. The proof is in the putting...heh!
In regards to your queen taking to her - there is just no telling with cats. Sometimes, even if they don't like the new family member, they become resigned in time to their presence, and reach some kind of an agreement with each other. There are bound to be fights, at least in the beginning - those are needed to establish a heirarchy.
I _would_ suggest that, if you do take the new cat into your home, you should pick a room your resident queen doesn't care for too much or at least is seldom in, and keep the new cat in that room for a while before she is given the run of the house. Keep the door to that room completely shut for at least several days, and then fix it so the door is cracked but won't swing open for at least several more days. This gives them both some time to establish territories, scope each other out ect.

just my 22c-worth
Tracy/Eluned (pick one)