In this case, I think, deal with it means that they are getting married and whomever they are talking to needs to accept that. I assume that the person they're talking to doesn't agree with their relationship for some reason and wouldn't approve of them getting married?
Child: I don't want to go to school.
Parent: Well, you have to. Deal with it.
The parent is telling the child that they have no choice in the matter and they will have to accept that they are going to school.
It can also be used another way to tell someone to handle a situation. For example:
A: Someone needs to take the rubbish out.
B: I'm really busy right now, can you deal with it please?
B is busy and doesn't want to take the rubbish out so they ask A if they can do it instead (fix the problem).