I'm confused as to know what to say really. I don't want to put my situation onto yours.
We have been in a very similar situation. We had a stillborn son and a daughter who died neonatally, and the way PILs treated us at that time has resulted in us cutting them out of our lives.
It wasn't easy or done overnight, it took about four years from the loss of our son to walking away from them for good. Things had been difficult with them before that but losing the children and the cruelty we experienced from them as a result was the final straw.
I wouldn't say that we were the type to bear a grudge. It's not about a grudge, it's about protecting ourselves and the child we went on to have from two people who are cruel and spiteful and selfish and manipulative and controlling.
During the course of those four years, they drove me to have panic attacks and tried to split up our marriage.
Perhaps the difference here is that we live in the same town and you live very far away from your MIL.
But in all honesty, I disagree with you when you say this "I realise the situation between me and her is not ideal but I am concerned about how things affect the children more."
I think the affect on the children from maintaining a relationship with a selfish, manipulative woman is worse than not having one at all.
They see her refusing to speak to you and you still going out of your way to accommodate her.
They see her making and breaking arrangements and disappointing them, just because she feels like it.
They see her badmouthing every effort you make.
They see her being critical of you and getting away with it.
You feel that she would badmouth you to them if she had the chance.
They see her forgetting their birthdays, and you and your DH disagreeing in how to manage that. You can only try to manage that so far but as they get older they are going to know that she doesn't think of them and has to be reminded.
They see the damage she has caused to your relationship with their father.
How is any of that worth maintaining? She doesn't care about them enough to send a card or gift on time or let them have a nice day out. The affect of keeping a relationship with her only looks like a bad one to me. Again, I may be viewing this through my own experience and I'm not meaning to be critical of you. I just don't see what good you think they are getting from having her in their life.
But I think if that's the decision you have made and want to stick to, being honest with them is the way to go.
Tell them the truth about her. Don't try to protect them by pretending she remembers their birthday. Tell them she forgets everybody and it's not their fault, it's hers. Let your DH say that she's crap. She is crap.
When our estrangement happened one relative got really angry with us because, in her words, she was trying to keep the peace and we weren't rewarding her for it.
When I asked her whose peace she was keeping she couldn't answer me. Because she wasn't keeping our peace, she was treating us really badly. And she wasn't keeping her own peace, because she was angry and upset.
And that's what I see when I read your posts. You're trying to maintain a relationship for someone else's sake but none of you seem any happier for it.
Your MIL is still awful, you are still annoyed and upset, your DH is still arguing with you, your children are still being forgotten and treated as second best.
So while I'm not telling you to cut yourself and your children off from her, I am wondering what you and your children are getting out of this relationship that is better than not having one.
And I would suggest looking at that and asking yourself what you think your children will gain if you are able to manage her 'forgetfulness' for a few years and keep it from them, when ultimately they're going to get older and realise it was all you and not her anyway?
You can all still have a relationship with her, but it will be more realistic and honest on your side. What she makes of that is up to her but why are you and your husband working to maintain an image for her that is false when she clearly doesn't care enough herself to make it real?