Keeping goldfish "properly" is one of the most difficult things in fishkeeping, IMO. One of the reasons is that there is such variety in color and type...and personality...that it's hard to have the self-control to maintain them within the proper limitation of numbers that make for good goldfish keeping. I'd say, honestly that two is the number that your Mom should keep. If she gets them small, I'd even go as far as to say three. They will grow, of course, and they may get too big so that you have to remove one...or maybe even two. But, from having kept fancy goldfish for many years, I can say that if there isn't any over-feeding and over-filter like crazy...you'd be able to have three in the tank for a good amount of time without any problem. Just be prepared for the possibility...the likelihood...that a bigger tank will be needed at some point.