I have to agree that even if they are small a 2 gallon is much to small for two goldfish, and while there are some filters out there that could go on a 2 gallon tank they would not provide adequate filtration for messy goldfish. If these are single tailed goldfish (the kind you'd buy at a fair or in the feeder tank at a pet store) they are actually recommended to have 15-20 gallons each. And one word of advice, stay away from undergravel filter, the kind that look like a grid and go on the bottom of the tank, these are not a good option for goldfish and will cause you lots of problems.
You might try bringing your mom to this site and letting her read up on the caretaking of goldfish. Even though the fish are tiny, having them in too small of a tank from the beginning can actually stunt their growth so that they do not develop properly. Fish release a hormone into the water and if there is too much if it because the tank is small, they will not grow properly which can endanger their health. Here are some links to show your mom if you think it would help, plus they are good for you to read as well:
http://www.kokosgoldfish.com/tensteps.htmlhttp://www.kokosgoldfish.com/care.htmlhttp://www.kokosgoldfish.com/Filtration.htmlhttp://www.kokosgoldfish.com/cycle.htmlYou can get a ten gallon tank, hood and a decent filter (make sure it filters at least 100 gallons an hour for a 10 gallon tank, or 10x whatever the gallonage of the tank is) for less than $40, especially from stores like Wal mart. Be wary of some of the fish tank "kits" though, the filters that come with them are often not strong enough to keep a goldfish tank clean. Even a Rubbermaid bin with a filter is better than a two gallon tank.
I have this filter on my 2 gallon betta tank, it works well, but again in an overstocked 2 gallon you are going to be fighting a losing battle no matter what kind of filter you get, It is called the Red Sea Nano filter:

If you aren't too attached to these particular fish you can usually take them back to a pet store and they will take them, and sometimes even give you store credit. A betta could live in a 2 gallon tank, so that is always an option, but of course if you are already attached I know how that is!
Lastly, I just want to say that I found this site because I had a goldfish in a 2 gallon tank who got ill. She ended up dying, and I decided to learn about fish keeping, and through this site have learned so much plus I now have a great , but very addicting, hobby! Most of the people here end up finding this site because they have a sick goldfish. What is wonderful is that you are asking these questions now,
before your fish are showing signs of illness. I know this is a lot of info to take in at once, but once you have a big enough, well filtered tank going you will actually end up with much less work as far as water changes and stuff go. Plus, you can decorate!