The conversation ( with whomever) should have happened BEFORE they purchased. Did they completely spring this on you or did you already know they were looking at places while visiting?
Be firm, stand your ground about encroachment of space and TIME!
I understand your "dilemma" as I had this conversion with my last remaining uncle (my late dad's brother). I flat out told him to not move back to my ( his old) hometown simply because I live here/ nothing would change/ NO the cousins do not see each other except Xmas eve and I'm not the young girl you remember as I have my own family w/ a grandchild living in my home/ my own health issues and an elderly mother in a memory care facilty to visit often. In other words my plate is full! Shortly thereafter, I'm looking at a senior living apt for him- in my hometown. OMG! I was lucky, he ended up about 40 miles away . YES, I see him about 3 or 4 times a year and that's enough.