I have asked my mother and explained that they would just be here for sleeping and evenings and that they don't expect me to be with them all day. She agreed and knowing her, will probably take one day off to show them some MinorCities that are difficult to reach by public transport.
So they are staying at my house in the end. They know I won't be able to see them during the day and are fine with that. I think in the end it's more about saving money, while I was afraid that they wanted me to be there for them all the time.
And for those who were wondering, we were exchange students (the three of us) at the same time and became very close, but with finances and different schedules it's become very hard to see each other. We try to every year, but it doesn't always work out that way. Espcially not with her, since she is the one who lives the furthes and is the most expensive one to travel to.