The more I think of this the worse an idea it is.
You would own a house 50/50 with your child. Let's say mother and son to make it easier.
Even if you get on very well, your son decides he wants his half so he insists on selling the house. He would have to take legal action, but it would eventually succeed although there wouldn't be much left for either of you after High Court costs.
Mothers and sons who have gotten along fine for years, sometimes fall out.
You want to bring a new partner to live with you in your house, and your son forbids it.
He wants to bring his partner to live with him in his house and you forbid it.
Either party could make like unbearable for the other.