If you asked me, "Did you ask your boyfriend's mother if you could marry her son?" I'd say no. I would hope that in the case of husband 1, she would sit me down and say, "That's not a very good idea. He's very unstable. Have fun with him, but don't marry him."
I have a very religious brother who is arranging marriages for his 12 kids. The first five are married off and so far, all the marriages seem to be going well. Here's how it worked: 1. My brother and his wife tell the matchmakers for his sect that he has a 19 or 20 or 21 year old child ready for marriage. 2. Potential mates are found. First both sets of parents meet one another. Mothers and fathers participate equally. If the parents get along, then each set of parents meet the potential spouse of their kid and think about whether their son or daughter will get along with him or her. 3. If the parents then want to go further, they introduce the kids to each other. I believe that they are allowed to meet privately away from a chaperone and talk. That is usually enough. If they like each other after a couple of hours, the announcement is made. If they don't like each other, they move on. No one is forced to like the other person, but usually they do. In most cases, this is the first time they've talked privately with a member of the opposite sex that is not a relative. The match has been carefully screened by a lot of people heavily invested in this being a good match. I said to my brother - they only meet once before deciding? He said, "Sometimes twice. Why would you need more?" Anyway, he's five for five so far and 7 or 8 new babies have been born so far. They live in Jerusalem so I'm not that up-to-date. Maybe I should be. My point is this: In that culture, the boy does not ask the father-in-law permission to marry his daughter. The parents set the whole thing up. The boy and girl have to equally agree though.
In any event, it's a good idea to grow close to in-laws if they are nice people.