Another idea is to run the AC inside and just let the heat it blows out to blow inside the box.. making it truly sealed. But wouldn't that negate the cooling the AC would be doing? Cool air out and hot air out? And these things REALLY do push out some heat too. I just don't know if that would be effective at all. If y'all think it would be worth it.. lemme know. Cause that's a possible viable option if the cool would take out the heat it puts out.
If I am reading you right input and output in the box with no exhaust you will actually raise the temp. Significantly.
Do you understand the concept of a mini split? They are a heat pump with all the hot stuff outside and cold pipes that run to the exchanger inside. This type of arrangement is the only thing I can recommend with a sealed grow in a bedroom. You cannot use your bedroom as a lung room for your ac unit your house ac will not keep up.
I hate to be a downer but I would recommend you simplify on the first run. Have you put everything in except a plant and measure temp and rh as is? You may be forced to be unsealed with exhaust on the first run. The problem there is your bedroom is gonna get hot and muggy. If you can’t use ac for now will your system reach a good temp/rh range with your bedroom as a lung room? Is it too hot to sleep?
You might be tempted to exhaust with a blower out the window. Your dad might object to that because it really screws with the house ac. Maybe some middle ground can be found but power everything up and see what ya got to start with.