I looked into this further for you and see the option for the toddler to ask an unrelated adult to adopt them! I wasn’t aware of that feature. From what I can see, I figure these steps should do it.
1. Age baby to toddler - have your adult Sim bake a birthday cake (costs LPs).
2. Select the adult who owns the home you want the family living in, and have the toddler ask that adult to adopt them!
I like having this option but it takes longer because birthday cakes take a day to bake, plus cost LPs. So the first option allows you to keep the baby, and costs Simoleons and no waiting, and the second option ages the child, and costs time and LPs.
Good luck! Would love to know if you achieve your goal by the second method! Thanks for the insight!