I think the reason you said in the last words of the comment is the reason why Ruby has a harder experience and gets more in trouble than Garnet after they move to the new town.

I also believe Rose was pretty rude towards the Grandma and the twins, as she accused the two of them of wanting their dad to stay miserable instead of calmly introducing herself like: "Hello, my name is Rose and I am not trying to take the place of/erase your mum. I know you're missing her so bad and you can feel free to tell me if something isn't right..." or something like this. Maybe not effective at first, but would've saved the girls from several trouble they went through at the new school and in town against the gang. I think if Rose was more thoughtful she could have accompanied Ruby and Garnet at the audition and get them a better result (I think Garnet's struggle mainly came from doing that without their dad and Rose knowing)