In a difficult position
You should not be made to feel that you’re stuck in the middle. It would be nice if your husband understood that when he is sick enough to be hospitalized that YOU might need the emotional support his family could offer. But since it’s not going to happen, he should make plain to his family that HE prefers to be the bearer of this kind of news, and the reason they aren’t hearing it from you is because he wants it that way.
Missing my sister
I don’t blame you for feeling hurt, because apparently your sister isn’t interested in having the kind of contact you would like. It may be that her husband is ultra-controlling — hence the constant interruptions from him — or that her household is so disorganized she’s in the middle of a whirlwind.
If you haven’t already, write her a letter and express your feelings. It’s one way of getting your thoughts across without being interrupted. I don’t think 30 minutes three times a year is a lot to ask of her. Propose setting a specific time to talk when her kids and husband aren’t around. Then cross your fingers and hope she sees the light.