How do I know if another player approves of his/her sim moving into my household?

It's not a good idea to use others sims in this game for the reason your posting. If the other player is not willing to give you their sim , your stuck in your situation. Your only option to get out of the relationship is to do mean interactions until your sim and theirs break up/get a divorce. This way your sim can have a new relationship with anew sim. It's possible the other players sim is already married in their game. It's best you make and use your own sims.