Did you tell them that you were just planning for them to stay only 3-4 days? Because in the matter of how much time they are going to stay I think it's because of lack of communication.

Also when inviting someone with a baby you should be prepared for all that it comes with it.

But for all the other things you are right. They are totally rude and disrespectful. You have two options: Be honest and asking them that they can only stay for a few days and to start cleaning up after their mess so you all can enjoy their stay. Or come up with a lie: we have to paint a room and I don't think it will be good for the baby to stay around, we were planning a trip alone during a few days, we have to leave to attend a family emergency or whatever. Or you could just say that as much as you love them being here, you didn't plan to have them here for so many days.