He laid the groundwork for it in the last episode, but now it really seems like Dean is ready to kill Rio on Good Girls. Last week, at the end of the April 7 episode, Dean seemed to realize that Beth had slept with Rio, and it broke him a little bit (which is rich considering Dean cheated on Beth, like, a bunch.) The next day, Dean marched down to his son's Krav Maga class and spoke with the teacher — a rumored former Mossad member who worked in the Israeli version of the CIA, basically. When Dean starting asking questions about how to "kill a dude," it was clear the dude he meant was Rio.
As of the April 14 episode, Dean was still very much on that track. He tried several times to convince others that he wanted Rio dead because Rio shot him, but that's not the whole truth. Dean didn't care that much about Rio until after he slept with Beth. This is toxic masculinity at work. He's only angry because Rio stepped on his "territory." Beth, of course, owes Dean no loyalty, but you can tell that this is how Dean is justifying things to himself, and how he's going to attempt to justify murder.
In classic Dean fashion, though, he's too cowardly to do it himself. The Krav Maga teacher gives Dean the number of a "friend" who can make his problem go away. Dean also tries to recruit Ruby's husband, Stan, to take matters into his own hands. But Stan looks concerned that Dean is heading down that path, and changes the subject. Even the Krav Maga teacher is concerned. Before giving Dean the phone number, he suggests Dean just get a divorce, and warns that this "friend" could easily turn on Dean after the deed is done. But Dean doesn't seem to care. He'll stop at nothing to keep Beth away from Rio, even if it means hiring a hitman. At the end of Sunday's episode, Dean dials the "friend's" number, which could mean he'll set this whole thing into motion as soon as next week.
But Rio is smart. He won't be easy to kill, even by someone an ex-Mossad member knows. And you can bet that if Rio catches wind of Dean's plans, he's going to make life hell for Beth, Dean, and their family. That being said, it's possible Dean will chicken out before things get that far. Though the show tries to give him some redeeming moments, Dean is a cowardly man. The only time he kinds of shines is with his children, who could be another reason he doesn't end up going through with it.
If Dean can connect to that "good dad" side of himself, he may see that hiring a hitman to kill his estranged wife's lover/criminal partner is maybe not in the best interest of his family. He can't parent from prison. It's also this side of Dean that may be swayed to see Rio in a new light. After all, Rio is a dad too, and Manny Montana, who plays the character, told MEA Worldwide that Season 2 will introduce Rio's family, who are "very important people" in his life.
If Dean ends up seeing this, he could soften up a bit and let Rio live. Dean isn't cut out for murder, especially for the dumb reason he's given, which is just that he's jealous Beth and Rio hooked up. So as serious as Dean thinks he is about having Rio killed, it's unlikely he'll be able to go through with it in the end.