Hi there. I am sorry to hear you are having such a difficult time with your toddler.
Toddlers (well children in general) are very sensitive to changes and having a baby and moving to a new house is a very big change which most often results in sleep disturbances. I remember when Jasmine was born, Isabella refused to nap as well and she was only 14 months back then. We also had frequent night wakings & we were all exhausted. Do they share a room because you could try and put a white noise machine in the babies room to block out the crying. I had to do this and we have a fan running in Jasmine's room as Isabella often woke her from the screaming and crying as well. Humidifier is also another idea as white noise.
When the baby was asleep I made sure that I spent every minute with her, playing, reading books and in general making sure we were bonding again. When you have a baby they get the feeling that they are loosing you to someone else. Try and make bedtime ritual a nice one as well. Lots of cuddles and kisses and explain with every step what he will be doing next... I do this with Isabella "after a bath, we're going to read some books then go on the potty, and then lie down to sleep".
When he is up in the middle of the night, you will simply have to lead him back to bed every time. Say something like "Its still night time and you need to go back to sleep". You may feel like its never going to end but try to be consistent. He will eventually learn that no matter how many times he comes out, the only reaction he will get from you is taking him back. Try and not have a conversation with him - just simple things like "you need to sleep, its night time", or something along those lines. I would do the same for naps as well. I would do it for the duration of the nap because if you give up in 30mins, he will think thats the norm. You can tell him that he doesn't have to sleep if he doesn't want to but he is to stay in the room for some "quiet time" until you come to get him.
Have you tried maybe a reward system where he can get a sticker for every night he stays in his room and after 3 or so stickers you can give him a reward, like a new toy or a treat.
You might also want to introduce a night light with an alarm and explain to him that he is not to get out of bed until the alarm goes off in the morning.
In regards to the new room - have you tried asking him what he would like to do to make his room more comfortable? If he has a favourite cartoon character you could try and get some posters on the wall (or something) so that it is set up in an environment he's want to sleep in?
I would also bring the bedtime forward to 6.30 - if he hasn't napped for 9 days then he must be getting overtired and that also plays a factor.
If possible I would also try to get dh involved so that you can get some rest at night.
Sorry for the long post - hope some of these suggestions will be helpful to you
Let me know how everything goes
Layla