Plee, my situation is identical!
I too have been seeing someone else (for about 8 months), my stbx doesnt want the divorce and we too are still living in the MH but separated. We have a decree nisi though.
I took the plunge, invited my new partner to a couple of short meetings with my boys (age 5 and 8), one in a soft play centre and another when I went to look at a new car and actually really needed a second opinion. He spoke very little to them, allowed them to check him out naturally and simply offered short fun conversations about things like 'cake' and other stuff they liked. I gave it a few weeks and then invited him to join us for a weekend away. Was risky I know but I honestly didnt think there would be a problem and there wasnt. They all got on like a house on fire!!!!!! When I got back obviously ex found out he'd been there. He was not pleased and accused me of all sorts of bad behaviour. In my heart of hearts I know that Im doing the right thing, Ive behaved well in front of the children not so much as holding hands in their company, theres plenty of time for all that. Hes a good man, loves me like no one else has and is interested in me, my life and my children, Im not going to ruin an opportunity like this just because my ex wants to control what I do (always has done).
If you believe in yourself, your decisions and can justify your actions to yourself, do what you think is best and you wont go far wrong. Ive grown up so much since I started the divorce process, I now have self belief and it feels good

Goodluck!