I wouldn't block him from Facebook as he could potentially one day turn that around to make it look like you shut him out (even though we know that's not the case here.) It's just something he can use against you in the future if he ever wanted to. He may eventually decide he wants to be in his kid's life again, after months or even years of not putting effort in and that is HIS choice - you've done everything you can do. However, it sounds like he has a tendency to blame problems on you and you don't want him to have even the slightest evidence against you if you were to ever end up in court.
What you could do instead is remove him as a friend, and that way any messages can be sent to your 'other' folder and you don't have to read them right away.
It sounds like you have a good head on your shoulders, keep strong for your 2 adorable children