In your situation, I would filter them out of facebook posts (the legendary soft block) until this issue is resolved.
The way they are behaving towards your husband is emotionally manipulative and obviously upsets him. "We'll be dead soon" is flat out emotional blackmail.
I am guessing you have absolutely no other childcare option, because otherwise it would be a lot easier to address this assumption that they are somehow entitled to your nuclear family time.
They aren't. It's both reasonable and a sign of a healthy, functional extended family to be around on family time/family outings sometimes. But put sometimes in bold there.
I know I must come off as terribly unsympathetic to your ILs, but they see the kids at least once per week guaranteed from your description. Honestly that is a pretty massive amount to see family that don't live with you. There are loads of GNers reading this post who would be over the bloody moon to see grandkids that often. Or at all.
Seriously, what is their expectation of how often they should see the kids? Can DH explore this with them non confrontationally? It seems like you and DH both work - is there no understanding on ILs' part that you as the kids parents need and want some time alone with your own kids at the weekends?
There seems to be a terrible mismatch in your and the ILs' expectations here. Hopefully you can explore that in a non confrontational way and get on the same page.
The issue with your dad is a complete non issue. He sees them what, six times a year whilst ILssee them at least once a week? Moreover, how is it their business when and how you and your kids see your dad? You are an adult, not their underage child, they are not the keepers of your schedule. I would honestly not even engage with this childish nonsense over your dad's visits. Would they prefer a schedule of visits like your dad's - once every other month for a couple of days? I bloody doubt it.
Have DH handle this in as calm, sensitive and respectful a way as possible whilst making clear that you WILL have nuclear family time and you will NOT be shamed or manipulated out of it.
I hope this all works out for you. Hopefully it really is just an issue with unrealistic expectations on their part.