Not generally a popular view on here, but if you're serious about him, I'd just tell the kids. It's not your ex's decision.
I met someone last September, and as he was doing some work at my house (it's how we met, yes, sounds like a rubbish porn film plot!) he met my daughter too. We very quickly started seeing each other.
My daughter is 4, so didn't question us going out for the day with his child, also 4. I go out with friends and kids all the time with her.
After 2 months, I told her "you know x? I like him a lot, I think I'm going to ask him on a date". She said "that's exciting mummy, he might be your one true love!"
Context: girl is Disney obsessed at the moment!
I've told her what a boyfriend is - someone you like a lot, you want to know more, but you can't know if you love them until you know them really well.
If he hadn't had PR of a child the same age, I would have waited.
If I thought she was likely to be upset, I'd have waited.
If I thought me breaking up with him would upset her, is have waited.
I accept that a revolving door is bad for her, so if this doesn't work out, I will have to wait longer next time even if next time is my one true love!!
But no-one can judge her personality and feelings as well as me, and it's been lovely. We do stuff together quite often, he has now stayed over with her here once too. An older child might have been different, or a different personality. She gets loads of time 1:1 with me. She's really excited when I say "shall we see x?". He's quite low key around her - DEFINITELY not playing daddy.
Sorry - going on a lot! Thing is, all my decisions were based on what I thought was right for her - and yeah, what I wanted to. What her father thought was neither here nor there. Make the decisions that are right for your family, not him.