EDIT - it's a fast moving thread and I see you've already answered these questions
Are the children on the cash booking or the Avios booking or is it one of each?
In this situation it wouldn't hurt to ask, but be prepared for them to say no.
Depending on the age of the children you might want to ignore my suggestion of two going through F wing and two going via fast track to the club lounge and instead all head to the club lounge if they're unwilling to let all 4 of you in first class