No it is not normal but dysfunctional.
You likely have come from a family of origin where thankfully this sort of dysfunction his parents are showing you is completely unknown.
What does your DH think of his parents now, particularly his mother?. Does he want a relationship with either of them now?.
If both your parents are nice then keep up the relationship with them. Your children will also thank you for doing so as well.
They're his parents so its basically down to him to deal with them. If he cannot or will not do this then your problem also lies with your DH as much as them. Some men who have been under the conditioning of overbearing and or controlling mothers their whole lives (or with an enabler or bystander of a father to boot) do find it very difficult to actually break away from this and be their own person. Fear, obligation and guilt are but three of many damaging legacies such emotionally harmful people leave to their now adult offspring and he may well be in FOG with them.
He may well continue to maintain some sort of relationship with his parents but he may well not and it does not follow that you or by turn your children at all have to do so. Your boundaries re them need to be a lot higher than they have been to date; emotionally unhealthy people like these take full advantage of nice people like you who are unsure about rocking the boat. You would not have tolerated any of this from a friend, his family are no different really.
Why do you write that NC is not an option?.
Forget the "not my circus, not my monkeys" attitude as well, it will not help you here. Both of you need to adopt a clear and consistent approach to them, anything less than that will not work. You both have to support each other equally and stop worrying about him potentially denying her access.
Who made it clear to you that MIL will not be helping with the children?. Sounds like a good thing really given her own awful behaviours towards her son and by turn his own family unit. She has really done you a favour by not "helping" out.
Why are you concerned that your DH would stop her seeing them?. You cannot and must not apply the "normal" rules of familial interaction to such people like his parents, the rule book goes out the window when it comes to dysfunctional families. These people certainly do not play by "normal" rules. Grandparents in this country have no automatic right to see their grandchildren anyway.
These people like his parents were likely also rotten as parents and are not up to much as grandparent figures either. Your children need positive role models instead, not some grandmother who is already making odd comments already with regards to your first child (this may be favouritism on her part).
Why would he be wanting to plan anything nice at all for them given what happened over the Christmas period?.
There is no law to say that you have to at all continue seeing people at all who treat you like rubbish. Also seeing them also allows them to continue treating you like rubbish and it also sends mixed messages to your children. Some families are just not very nice, it is not your fault his mother is the way she is. Her own family of origin likely inflicted that damage and some people never seek the necessary help they need.
I would suggest you read "Toxic Inlaws" written by Susan Forward to further understand the dynamics of power and control that are really going on here.