Okay when he's playing leave him.
One of mine (I have 3) Would wake up and hum - progressing to singing nursery rhymes with age - for anywhere up your 2 hours a night anytime from midnight to 2am.
If he's playing he may he able to self soothe back to sleep with time. So leave him to it. My fingers are crossed for you.
When he's screaming no eye contact and shushing noises - other soothing noise you use - don't talk - one of the best bits of advice my Nan ever gave me. Yes it was hard but it worked after a few weeks perseverance. The length of soothing time lessened and lessened.
I would pick up and rock again no eye contact.
When he wakes and is upset in the morning or after a nap plenty of talking eye contact.
Setting apologies should have been clear I meant with you or nursery?
If he's in a nursery setting it can be a lot harder to establish your own routine.
How long has he been in his own room?
Some child a just don't like it (my first I caved and he didn't go to his own room till he was nearly 3 - slept in own bed in my room)
3rd was easiest but she went in with her sister so still had other noises.
Can you try to move the first nap to a slightly later time and keep it to a hour? Thus adjusting the later nap time.
Try and do things to tire him out before second nap so he is more likely to go down.
He may need to have one large nap in the middle of the day rather than 2 shorter ones. My first had less bad nights with days of establishing this routine was hard to keep him away the extra bit the first 2 weeks.
Is he in the pram or cot?
Second napped in pram only as she saw the cot as night bedtime and would be a nightmare if she'd napped in a cot or travel cot.
Naps are a hard one as I understand you have your routine that is individual to your family and what works.
I had a different experience with each of mine. What i did may not be an approved method but it worked for the child that needed it. I grew up with a strict bedtime routine and so have my children, that included as babies. But it had to be done there was a routine when my 2nd was born, I had to get the 1st to school.
If you have family around ask them what yours, your mum's sleeping habits are like. And for tips with what they did.
Again what I've suggested may not be something you wish to try I felt like a cruel mum but once they started taking less and less time to soothe, started to self soothe/go back to sleep themselves after playing/singing for abit. Then slept for longer and longer it was worth it.