MIL not putting in effort and then complaining she feels “left out”.

This exactly.

You know what you are doing @Conversationalcheddar.

A woman who expects a newborn to be driven to her because she doesn’t like driving will never be reasonable!

Maybe DH could get social media and he can do a soppy post. You can help him.

OP I think I would either go with what a PP suggested and just ask her how she would like to be more involved or just ignore it completely.

I'd also be blocking the shitstiring SIl from my SM as well.

I had to have a little chuckle at that too! Being nearer 70 and running social media accounts for several organisations! BTW OP YANBU

He should reply to his mum directly rather than allowing his sister triangulate and shit-stir.

He definitely needs to really think through what he wants from the conversation.….
At the same time his mother sounds like a very immature person. She is jealous of someone doing what she won’t and doesn’t want to do.
There is zero, absolutely zero, point in trying to have a constructive conversation with a person who is going to leap down your throat (which she will - where has SIL learned that from!)
Maybe he can open the door with “SIL said you were unhappy about Cheddar’s IG post, do you want to talk about it. Or was it just venting a bit and she shouldn’t have mentioned it to me?” Then it puts the ball in her court - if she doesn’t go any further just forget about it. Her emotions are not yours to be placating and soothing.

The other thing of course is about the quality of the time. My kids spent approximately equal time with both sides of the family. But with my parents it was always better because they were interested in the kids themselves as people. Until quite late in the teenage years they were seen by PIL as a task or burden, and it isn’t about which side of the family it was, there are great aunts and uncles that they enjoy visiting: because those people are interested in the kids themselves.

I'm the same thoughts. It's a pleasure to spend time with my grandbaby. I don't see it was giving a break to his parents.

It's important that grandkids actually knows you and feel comfortable with you to step in for "emergencies' so that poster is unlikely to have that problem either. Kids sense uninterested family members.

OP and her parents come from a different culture where this is healthy and normal for them.

I'm presuming that OP will probably provide hands-on elderly care for her parents when they need it.

To me it sounds like neither if them have actually cut the apron strings.

Agree. My mother lives a short drive away and we’d never use her for weekly childcare, but many of her friends are, and she tells me they felt they couldn't say no to the requests, but they fall out of the local community as a result - they are unable to join in the coffee mornings / walking groups / book clubs / Pilates etc which make up so much of the village life as they have toddlers in tow. They don’t get any say over when they go on holiday either. She said it’s very sad, and they see it as taking massive advantage.

You obviously have a very hands-off approach to being a grandparent which obviously suits your family and you are still working.

OP and her mum come from a culture where the grandparents are very involved in the care of grandchildren so this is normal for them.

If one of your DILs posted on social media thanking her mother for all the help she gives with her grandchildren, would you still be upset and offended given that you wouldn't dream of providing hands-on care and support for your grandkids?

And if Mil did nice things for the family like her mother does then yes maybe she would

For you, possibly. Everything about the OP's post says she's loves it, and her DH''s reactions say he has no objections either.

Yanbu of course.
I think if I were your Dh I would respond with "I'm sorry mum, I had no idea you felt that way. I had the impression you weren't keen to be involved more, especially when you said you were done raising your kids. Please can you let me know what you have in mind if you'd like to be involved more?"

Then see what she says.

I think this is one of these times it's important for him to use I and not we.

Course it isn't healthy. Its suffocating.

Agree. The OP’s mother is staid to be doing what the ‘needs’ to do, implying that MIL ‘needs’ to act in a similar manner if she wants to be included.

Who said its not 'healthy' for 2 adults to call several times a day if they both want to?

While I would argue with the use of "needs to do" by @Mapletree1985, it's the OP's mum she's referring, to, not the MIL.

Who said I wouldn't have them overnight? I'd love that but as part of a loving relationship, not as a contractual arrangement to provide childcare or breaks. If DD or DIL were ill, of course I'd have their DC, if it was for regular weekends away and date nights that would be a different matter.

We have one on the way, and I've always been clear with the DC that I shall not be an alternative form of childcare.

You have Mothers on the opposite ends of involvement and extreme examples at both ends. Both magnify how each behaves. Without doubt the MIL is disinterested but getting the balance correct can be hard with grandchildren, I don’t have any but have observed my much older sisters grandchildren issues from the sidelines and seen the fallout.

She's made her choice

Recently I had to pull up my family on their involvement in dcs life despite living just as close as Pil who are amazing

Don't let people tell you that you should be putting in the leg work sending updates and photos

Doors go both ways is my moto

If she wants to be part of their lives and have posts made about her she is just as capable of making an effort and calling or messaging if the travel is too much.
My dgm, childrens dggm who is mid 90's can manage to email and asks for photos of them, can't manage to attach her own pics but that's fine.

A woman who snarls that she’s “done raising (her) kids” and won’t raise OP's and because she “doesn’t like driving” only sees the children 2 or 3 times a year can hardly be surprised that she hardly has any role in her grandchildren's lives. Ignore all those suggestions about trying to get her more involved as she seems to have almost no interest in your children and appears a deeply unpleasant woman. I think your SIL who drew your MIL's attention to the post is also likely quite unpleasant herself.

Is this what she ‘needs’ to do? If so I don’t blame her for throwing in the towel. If she doesn’t lay herself down as a doormat she’s not doing what she ‘needs’ to do?

So, presumably, when you become old and frail and require some practical help its perfectly ok for your children to then say they will only help you in a dire emergency and "won't be caring for you because we've already cared for our own children" because this works both ways....

Is that what the OP's mum does? Read the OP's first post.