Hi Lazycrockett.
It's possible to move the kids in with your Sim, but not while in-game until they are grown. You'll need to use Edit Town. You'll also have to find the kids somehow. One way is to invite the mother to visit, ask her to leave, then follow her home with the camera. Use Pause while following because she will get out of site fast. When the mother gets back home, take note of where she lives.
Once you have the location, go to the Main Menu while still in-game (the three dots in the lower left corner). Choose Edit Town. This will take you to a Map View of Bridgeport with tags on all of the houses and apartments. Click on the one where your kids live. A window will open that shows everyone who lives at that location, along with buttons for options. Choose the Merge Household option and follow through the steps. If I remember correctly, it will ask you where to merge them and you'll choose your own home. You'll be able to select which members you want to switch. Then just finish up and return to the game. The kids will then be in your household and under your control. It's been a little while since I've actually done this, so if I told you something wrong, come back and I'll do some research for you. But I think I have it right.
If you chose to just ignore the kids, they will be fine. They will grow up as regular townies in Bridgeport. You can develop a relationship with them or not, however you choose. Their traits will be random because you're not raising them and will not get to choose their traits as they age up.
Another option to consider for your single male Sim is adoption. Use the cell phone and select Call for Services. Adoption is one of the services you can choose. It's free and you get to choose the age and gender of the child. The Social Worker will deliver the child to your home in a day or two.
I'm moving this topic to the Miscellaneous Help folder because it's really not specifically about Late Night.
