I’m afraid I agree with the previous posters. A rabbit is a very long-term commitment, 10-12 years for a healthy long-lived rabbit. If you have lost interest in a hamster that only lives 1.5-2.5 years at most, how do you know that you won’t lose interest in a rabbit. The set-up costs for a rabbit are expensive, and if you can’t buy baled hay, hay is expensive along with their vet care. Your mum may not be able to afford those extra costs, and of course she has mentioned concerned with the dogs which is a legitimate concern. Accidents can happen and it would be terrible if it did. So sometimes it’s better safe than sorry.
Every pet should be important and valued, no matter how big or small.
If you really want a rabbit, when you have yourself settled after college you can get yourself into a situation where you can own one for yourself without restrictions of living with dogs as well.