Have you tried searching through your local classifieds and shelters? The A.S.P.C.A. seems to adopt them out fairly inexpensively while the S.P.C.A. up here in B.C. charges as much as buying one directly off of a breeder at times. At least if you purchased your guys off of the A.S.P.C.A with the usually low adoption fee, they should come spayed/neutered so you wouldn't have to incur that extra expense once you get them. Problem then is, you'll probably have to get funding from somewhere to get their teeth done at some point especially if they are younger ones you're adopting. With older ones, you can hope they were dropped off at the shelter after those details have been taken care of. Unless, of course, you were hoping to breed them, hence the boy for you mom, and a girl for yourself. In that case, I guess you'd have to look through the classifieds for rehomings or young pups from hobby or byb breeders in your area. Maybe try searching for pups from neighbouring states within driving distance from yourself so that you may check them out in person before buying.
If your mom doesn't know that she'll be raising a pup, and is not prepared for that, maybe buying her something like a new iPhone would be a better idea for her birthday? Then you'd even have more funds available for yourself to choose the perfect girl yorkie with that increased budget.