Hello JKB0306, and a warm welcome and sorry for the position you are in, as I wasn't too pleased myself when my sons had friends over and played music loud enough for the town to hear, it certainly didn't agree with me, especially when I was in depression.
If they are staying in your house for whatever reason that may be, then you set the rules, giving them an allowance one way or another on what is accepted, and if you don't want to listen to this loud music then there are ways for this not to happen and avoid a situation like you have to try and cope with.
If your mother gets ' gets angry and dissapointed/jealous' that she believes you are spending enough time with them, then explain about the other 5 days you're with them and allow them some benefits, but the music is definitely a no no and disconnect the unit.
Perhaps they can listen to it in a shed but I'm not sure how the neighbours will feel and they may ask them to keep the noise down, it's good you have them stay with you, but rules are rules and everyone has to abide by them.
Best wishes.
Geoff.