Although you've realized your mistakes, you couldn't take care of your past rats, and that's the only sure thing your mom knows. I also agree with Peggy and Zooy. No matter how well you take care of them, your mom is still in control, and it is simply unfair to your rats if she decides that they have to go.
If you still have a few years before moving out, there are other ways you can be with rats, if you like them enough. You can ask some rat rescues in your area if they need help cleaning, playing with, etc. You can work at a shelter that has rats, some pet stores take volunteers(you could probably even work in one, if you're old enough), you could post ads as a rat sitter for people going out of town, or find friends with ratties and visit them often.
In the mean time, there is always room for improvement. Browse our forums(Welcome! By the way, lol.) for, digest all the rat info you can find on the internet, and by the time you can get them- you'll be a fully prepared rat expert. I thought I knew all there was about ratties until my Charolette got sick. I knew enough to see the signs the second they occured, and rushed her to a vet. The cost for the visit was 80$, she was anemic from a possible fall in her cage(in her cage, yes. Witch wasn't that tall! Accidents happen, even with agile creatures.), so she had to be put in oxygen treatement, get fluid injections, stay at the pet hospital, and get antibiotic injections. All of this cost about 500$, witch I payed myself from a lucky fund of about 600$ I had, witch I was saving since I was 8 years old, as I am not old enough to even get a job yet. In the end, though I say this in heartbroken pain, she still didn't make it. Two days later, my other rat, Matilda, also had to be taken to a vet because she had a respiratory infection. Once again, 80$ for the visit, and 65$ for two antibiotics(she will be fine, I detected early and it's not very serious).
Although it was unlucky for both my rats to get sick in a matter of 3 days, it happened, and left me broke. Matilda is now alone, so I must buy her another friend so she isn't lonely. Rats are not cheap pets, and do not show signs of ilness(usually) until the disease is in a serious stage, because they are prey animals. Therefore, the second you notice something is long, they must go to a vet. You won't have time to make money mowing lawns, etc.(Considering you're young, you said you live with your mom, and considering you don't have money saved up). If your mom isn't willing to pay for vet visits, then it is simply safer and more fair for the rats to wait until you are in charge of yourself, and them.
On a last note, I know how you feel. Rats are amazing, and reading all these things about them just makes you want one more! I know, I used to spend hours on DapperRat imagining all the fun things I would do with them. But if you loved your last ratties, witch you did, then do not get new ones until you're sure they can have full, happy lives with YOU, not with someone who might have to rehome them after a few years.
However, if your mom does agree, and you decide to get a few;
-Have a suitable cage ready BEFORE you get them. I made a mistake of not buying one before I got Charolette(the one from my last rats was gone), and went frantic searching for one. So, naturally, I couldn't find anything, and Charolette chewed through her temporary one, so it was totally dramatic and frustrating. [Look at some of the posts on this forum for good, cheap cages- there are many about this topic!)
-I made the mistake of reading more about toys and hammocks than about diet, nutrition, bedding, etc. Although it may not be as entertaining, research nutrition and health signs, because they are the most important.
-Start a rat fund now. If you get allowance, say, 15$ a month(or whatever), put away a few dollars every week(or whenever you get it) into a special piggy bank. Keep putting some off everytime you get money, so that you have "emergency cash" to spend on vet visits. Trust me, when your rat gets sick(witch it will, sometime in it's life) you will not have time to make money. I noticed Charolette's signs on Wensday, at 12:30 a.m. I wasn't even sure if she would make it till 9 a.m., when her vet visit was scheduled. So start right now, because vets are not cheap.
:]