I think it's really lovely that you want your kids to be part of your new bub's birth...but unfortunately I don't think they'll go for it.

It's hard enough to get approval for a second adult in theatre, I can't see them coming at a child, let alone two. Their lawyers would have a coronary at the legal implications of having kiddos in there no matter how mature or well behaved.

You can always ask, there's never any harm in asking. If they say no, you'd probably have a good chance of getting them into recovery as a compromise. That would definitely be worth a shot.

All the best for a wonderful birth.