I would put Mr and Mrs X, Miss A X, Mr B X and Miss C X, as it's lovely when you are a child to get an envelope through the post addressed to you, but also as it makes it clear it's for all the children as well, if you are inviting them. Of course if they have 5 or 6 children, it might have to be 'and family'. Then you'll get the professionally offended MNers people who don't want to be called Mrs, who haven't changed their name, who have children with different surnames, etc., etc.,etc., but personally, I'd be pleased to be invited and not really too bothered about what was on the envelope as long as it was clear who you intended to invite.
Make it clear if the DCs are invited!! I had to do a lot of shamed faced apologising grovelling to guests as I put Mr and Mrs on the envelope and then had a card inside that didn't name everybody. Didn't make for good relationship with MIL...
I would do the adults as either by the version of titles they usually use (eg Mr and Mrs X or Ms Y and Mr X) and then add the first names of all invited children. Or I would use everyone's first names.
If the child was an adult still living at home, I'd put a separate invitation for them into the one envelope to the address. And if you have spare invitations, you could do that for any other children of any age you think might like an invitations their very own as a treat.