My mom got these dogs, but I want her to get rid of them.
For what reasons do you want her to get rid of the dogs?
Dogs are fucking useless and they bark a lot.
You should respect your mom's decision to get a pet if it makes her happy. You can move out when you are an adult and live a pet free lifestyle.
Ooh, I'm going to move out soon. I will show her.
If you're already planning on moving out then you especially shouldn't encourage your mom to get rid of the dogs. Let her enjoy the happiness the dogs bring her and try to deal with them until you move out. Sometimes it's good to make sacrifices for others.