This could be long.
I've long suspected my ILs are ND - my MIL in particular cannot make eye contact, lives her life by routines (and gets upset if they're deviated from), has very little conversation which falls outside of two or three main topics (how to get somewhere by road, how much something costs or a particular football team).
She also does not engage with me (or to be fair anything or anyone she isn't interested in) AT ALL - for example we recently went away as a family (MIL, FIL, BIL, SIL, DH, me and our 2 DC 11 and 12) and in the entire week she only spoke directly to me once! (I'd asked where the teabags were on the last day and she said 'I packed them.') That was literally it and is completely typical of our relationship - I have a job which involves chatting to people all day which I find easy and (on the most part) enjoyable so it's never been something I thought was difficult.
Prior to meeting MIL I would've said there was no one I couldn't chat happily to but when I have tried to engage with her in the past it's clear that she's so uncomfortable/ unengaged that it's actively unpleasant for her so I've allowed this situation to develop too I guess.
MIL amd FIL are very co-dependant so he will often talk 'for' her, and try hard to make things 'right' so she is comfortable in her world e.g she MUST have a cup of tea and a single malted milk biscuit at a certain time so he ensures this happens come hell or high water, no matter what else is going on (even if everyone is stuffed, having eaten recently).
I only realised they must likely were ND after having my eldest DC, initially we didn't spend a lot of time together so their 'quirks' and lack of engagement/ eyecontact/ interest in anything that falls outside their narrow window of interest I just put down to them being different to my own family - completely nbd because it didn't really impact me at all at that time.
Roll on the DC and we now (obviously) spend a LOT more time together - my DH tries to be a good son and wants his DC to have a relationship with his parents. He takes the children over for tea in the week, we visit at weekends and to be honest, we are pressured to invite them to pretty much everything we do as a family which wouldn't be a problem except I literally feel like I'm wearing an invisibility cloak the whole time and crucially on these occasions not one of the people involved actually look like they're enjoying it - my ILS are out of routine, stressed, unhappy, expecting us to follow myriad unwritten/ unknown rules that keep them comfortable, DH is stressed trying to keep everyone present happy, I'm annoyed that I've ceased to exist entirely and the DC are annoyed at their strange, cold, GPS.
The DC seem not to have a bond with them despite DH and I trying our best, throwing them into each others' orbit constantly, reminding the kids to be kind and loving "wave to grandma and grandad", "don't forget to say thankyou for your dinner boys".
It doesn't matter to me that my ILs and I have no relationship, that they seen even to struggle to relate to my DH (their own son) but I recognise that they love my DC and are trying hard to connect in their own way. The problem is that its almost like they've learned to grandparent from a PSA entitled "how to grandparent a human child" - they are trying to do the right things but it falls flat.
MIL spends her time pottering around doing little tasks over and over to avoid engaging (endless washing up of a couple of spoons or cups - turning washing repeatedly, taking it outside to air, then back in if she thinks it is grey, then laying everything out again) - I secretly think of her as HoloGran because like a hologram she looks like a normal person but it can feel like she isn't there or she's behind a screen.
FIL puts on a fake jolly bluster that is obvious and uncomfortable for everyone, perhaps in an attempt to compensate. He can't talk to the children 'normally' - for example on the recent holiday my youngest DS scraped both his knees very badly so he and I abandoned the preplanned trip to the beach with everyone else (sand!) and stayed home to patch him up - we were watching a film in the living area when we heard FIL return on the lower floor, I heard my DS say 'oh no, it's him' and proceed to pretend to sleep on the sofa to avoid him. I was just about to tell him not to when FIL marched in, up to him and shouted (Brian Blessed style) "HOW'S THE PATIENT?" - he kept shouting it until he came right up to him. DS looked annoyed but said 'OK thanks'. I wish he could've known to just come in normally and speak to him at normal volume would get a far better response but I have no way to convey that.
If you've made it this far well done but I think I just needed to highlight that while they're trying, because they have no interest in me I don't know if there's anything at all I can do to help the situation/ encourage a connection. I was always close to my GP and it hurts to think my DC don't have that.