Hi csr mel
How old is your mom and how long ago did she keep those guppies?
Sometimes our memories play little tricks with us and we remember things a little different then they actually were. Perhaps it was a 5 gallon tank? That's a very small tank, but it's still 5 times larger than the one gallon she told you about. I'm not sure that they even make a 1 gallon tank.
Also, the guppies were not always as big and as fancy as we know them now.
I remember when they were very small and did not have the long flowing tails they have today. They looked much like the "feeder guppies" that we have today. I don't know exactly when they started to change, but perhaps someone else does.
Fish keeping is partly an art and partly a science. This accounts for some of the different opinions on some topics. The science part is pretty basic and members usually agree with each other on things like the chemistry involved in cycling and keeping a tank cycled. What you get a lot of different opinions on is how to go about doing that. However, what ever they suggest, their goal is the same: 0 ammonia, 0 nitrite, and a minimum of nitrates. And, that's the important thing.
Fish are living creatures, and like most live things they can survive and even thrive under a range of temperatures and water conditions. Sometimes they will breed with water conditions one way and sometimes the same can be said for water conditions quite different.
This is why we share not only the science, but the art of keeping fish. The more you learn, the better you will be able to make educated decisions when problems come up, even if you have not encountered them before.
So you see, it is possible that neither one of you is all right or all wrong. I hope your mom will eventually get involved in a more positive way with your hobby and perhaps even join the forum herself.