For bedtime/naps:
Is he tired first of all? Does he 'need' the nap???
He is 3.5.... just tell him "I know you are trying to make excuses or waste time. It won't work. You can have Mommy stay with you and help you. Or I will leave if you don't cooperate." Say it calmly and in matter of fact way. Then stand up to leave. For my kids, that works.
Also, most kids, do need to wind-down first before napping/sleeping. So factor in this wind-down time and allow for that. No kid or adult, can just hit the pillow and pass out in 1 second.
To me, taking 1 hour to get him down means... he needs to wind-down first. BEFORE nap time or bed time. So again, factor in this time into your schedule of things and timing.
Most kids, need to gear down first, before sleeping.
And yes, they do pitter-patter about & quietly 'play', in the "process" of winding-down... which is fine. That is a part of the process. It is a process...
Also, kids at this age, are not mature yet... to just at-will, get themselves in bed and sleep. You have to 'cue' them, verbally and egg them on in their routine, prior to bed/nap. Cuing them..... that is what I do.
My son is 3.5 almost 4 years old. And he still naps everyday and goes to bed fine.
If I tell my son... "you have 10 minutes to do what you are doing, then put away... then get ready for nap time soon..." he will cooperate. But if I stop him suddenly in the midst of playing and say "NAP TIME now. Stop it. No playing..." he will put up a fight.
It is how you "transition" the child... and couch your verbal requests.... reasonably.
For him screaming at the gate and waking your baby: well, my daughter was 3 almost 4 when I had my 2nd child. What I did was simply "explain" to my daughter (like she was important), that when baby brother is sleeping... she needs to be quiet, or WHISPER. She understood. I ALSO... spent a ton of time, explaining to her about baby development in ways she could understand. I told her a baby cannot do things on their own/they cry/ they get hungry and Mommy feeds him/they cannot do what she does/they cannot talk etc. Each Month, I explained to my eldest, how baby is changing/developing and why. My daughter therefore was more understanding of the whole baby thing and irritations.
Next: why do your kids share a room at night? But during the day she sleeps across the hall?
You said your son screams until he wakes her up....
maybe sharing a room at night is not good... for him.
At this age, the child cannot be expected to be all quiet and still as a statue and not wake the baby. Especially if in the same room.
This is like mixing oil and water.
For pottying: well he can't poop in a toilet yet... and does not have that mastered. Boys are often later. My son is your son's age... and he has not mastered pooping in a toilet yet. But, because of what we went through with my daughter (who got constipated during potty training), I will NOT 'force' the issue. I am fully aware of the medical/physical problems a child can get, from being force to poop or expecting it of them, when they are not ready. For our Daughter, we did not 'force' her to poop in a toilet... but she, due to anxiety about it, got constipated and started to consciously "withhold" her stools... and it then causes medical problems... for which we had to then see a Pediatric Gastroenterologist in order to overcome it.
What makes it worse... although I understand... is that his pooping mastery, is dependent on the fact that he is going to school, in the Fall.
For which, he might not be ready.
A child, will not progress in pottying/pooping... according to a time-line on the calendar. And making it a focus... may even make it worse... with the child NOT wanting to even try at all.
all the best,
Susan