Welcome to our Forum, ceriebare.
You can't do what you describe if you're playing the same game file. When you switch to a different household, it will be in the same situation. The woman will show up as being in a relationship with the man. You can play different save files, though. When you start the game, just choose to make a new game and you can play a different Sim and have a completely different situation.
As for merging Sims with a household, you can do that through Edit Town. While in the game, click on the button in the lower left corner that has three dots on it. Then select Edit Town. Choose your family on the map and click the button for Merge With. Then select the household you wish to merge them with and go back to the game.
