I agree with NYGal...why not just unblock him? He is contacting you anyway, so except for the fun of being spiteful (lol), there really isn't a reason not to. Seems like it would be much easier to deal with texts than video calls, anyway.
Don't feel ashamed about begging him to see the kids. It's not like you begged him to come back to you. You are just a good mother who doesn't want to see her babies hurting. There is certainly no shame in that.
And as difficult as it is, try not to think about who/what he's doing when he says he's out. Like MB said, he could just be making it up to get under your skin. Just from reading your posts, it DOES sound to me like he does stuff like that deliberately trying to trigger a reaction from you. Don't borrow trouble.
