No fucking way. Your ex gets to act like a petulant child, can't even manage to have the bollox big enough to be in the same room with you, has been a total dead beat dad, and NOW he wants to call the shots?? Not a chance. Don't even consider it. This is not what is best for your children.
This.
And also... one of the main reasons this is not going to be good for your children is because given the above, the chances that he will either manage a few meetings and then not be able to be bothered or (worse) get completely into their lives and then flounce off again because his 'needs' aren't taking priority is very high. And really, that sounds like the last thing your son needs.
Try and speak to MIL about it. Basically, you need to protect them from his half-arsed idea of what it is to be a father as it's already damaged your son. Tell her that no you aren't being vindicitve, you simply want to see that he is really prepared to put the children FIRST and that he understands why you need him to prove himself on that front before you let him in as you will not risk them being hurt again.
These are her grandchildren, she should want them protected too. He is her son, she should know what he is like.
If she can't be on your side in this, then she's not really on her grandchildren's side either.