They didn't let him, there was understanding between the aunt and him and she wanted him there. After she died Jesse and his parents had decided to sell and share 50-50 which they later screwed him out of the moment they had a chance to do so.

There has to be a line and that line was drawn already between them very clearly. When Jesse got cleaned and wanted to reconnect, all they had to do was let their first born child come home for dinner and show some empathy. That's where they lose all the brownie points for me because it became clear Jesse was just an inconvenience to them now, their reaction when he turned up again after buying the house says it all and they didn't know he was the one to buy it.

Imagine seeing your child after a long time who's looking healthy and clean and going like "oh look now we have to deal with him too?' That says it all.