Edge if you haven't already i would offer him some reassurance that he is important to you and you love him very much but, he is asking too much and it's putting a strain on you.
I do wonder if this is coming from somewhere on his side, some feelings that happen in childhood follow us into adult hood, like abandonment issues when parents get divorced or even small things that are forgotten by others that we aren't even aware have impacted us and how we relate to our family members. That really is something he would need to talk through with you though if he needs to rather than this sort of behaviour.
Obviously you don't want to not have a relationship with him and the grandchildren so, arguing won't help so you need to teach him what you do not find acceptable and really develop some strong boundaries.
If he makes unreasonable demands on your time and energy you have to be firm, No justifications, no excuses, no pointless explaining "I'm sorry I can't help you today, I really hope you get x problem sorted and you are all ok/feeling better soon/able to find a solution"
We all need help and support from families sometimes but that's a balance between adults when we become them and we do what we can out of love, not obligation because we don't have any.