This scene is always infuriating to me. 

Firstly, Don feels emasculated and dispossessed of his house like a petty child just because his sister in law's family are a bit invasive with their three children, despite the fact that William was taking care of the chores and respecting the household. That's petty and egoistic.

Secondly, this whole scene and decision is just him using Betty's tantrum to pull a pathetic power move on William with his money and height to assess his dominance, disregarding William's involvement in his father's health for all this time. Betty was wrong to accuse him of wanting to "take the house for himself" when his concerns about his father were justified downplaying the struggles he must have faced not only logistically but also emotionally seeing his father's mental health slowly falter, then she played the victim making him a careless brother as if she wasn't the one who didn't give a shit about their father for all those years. 

To that not only does Don takes the opportunity to win back some points with Betty after almost losing her not caring at all about it being right or wrong, not thinking at all about the best solution for everyone or proceeding to appease the situation between Betty and William, he then proceed to humiliate William for no reason, just for the pleasure of lashing out and being superior, belittling him in every aspect, speaking to him like a dog, flaunting his money in his face, being disgusted by him doing house chores that he never does himself, and then putting him out to go back home with his family catching the last train without warning. 

I am surprised to see most people thinking Don was right in this moment rather than petty.