There are a lot of weird ideas on this thread that aren't the OPs situation.
The whole well I only ever stayed at my moms and never stayed at my dads so I don't see why any teen needs to be at their dads overnight. Or I never kept a single thing there, I just visited briefly and had a few things in a suitcase. In the OP, the teen still wants to come and dad seems to want him and he has had a space and belongings there all along. This isn't a case of a teen who only wants to stay in one place and doesn't want to spend time at dads
I moved out for uni and my parents took over the room - but this kid didn't move out for uni. It is taking his bed / space away from him while he still lives there - not after he moved out.
Or the well I only visit my parents, I don't live with them - you can spend time with your parents without living with them. Again - when you are married with a family, not the same as the OP case where is it s 18/19 yr old teenager. Many 18/19 year old teenagers still live with family.
Or the people are saying second kids don't count as much. No, I am saying that having a second family doesn't mean the first kids stop counting. All the kids have value from both families. It isn't a case of once you have a second family the kids form the first family lose their value as members of the family. All the kids should still matter.
On one hand, people want dads involved, then when they are involved - people are mad and say this isn't fair to younger kids and older kids should be booted out. Just because he has a mother and a bed there, doesn't mean that his other parent who is equally his parent shouldn't get to also have him around and have him also have a space there. The teen wants to still be around his siblings and his dad (and his step mom), he isn't wanting to only live with his mother.
And OP seems to have a better grasp on this than most responders. At the end of the day, their house is too small for the size of the family. There are four kids in the family - that is the reality of this family. Having more kids doesn't mean you get rid of the older ones to keep the numbers the same - it means the family gets bigger. If you value all four children in the family - you find a way to give them space in the home while they are still teens and in school.