We don’t have a good relationship with our roommates and we don’t want to go on the trip together. How can we ask more appropriately and be in line with our wishes?

Actually, there must be a reason for a bad relationship. Everyone has his own strengths and weaknesses. Some people’s shortcoming is that they don’t know how to deal with interpersonal relationships. Maybe this is his shortcoming, but You can't deny her because of this. Maybe through this trip you will find that she is not what you imagined, or maybe she is actually a very good person. Everyone lacks communication and must learn to be tolerant! I hope this can help you, and I hope you can invite her to go with you, maybe your relationship will change as a result.