Hmm, not sure if it will apply just to the kid. I had my Sim make a townie pregnant too. She was not a homeless and had a house so that I knew she wouldn't just vanish one day. I didn't feel like having the baby around either lol. This was before toddlers but I wouldn't want the toddler either, ahem. So I just invited the mom plus kid once the baby aged up occasionally. I invited the mom to stay the night and the child stayed too. Not sure if you can just invite the child. I know a child can ask another child for a sleepover.. so maybe adult/child will work too, especially if they are related? It would be interesting to find out.