Guilt!

[RoadRaven]

Mr Silver summed this up so succintly and accurately.

Talk about this as a trip, not a holiday. You can text supportive messages every day so they know you are thinking of them. Talk about/offer how they can have a trip as soon as things are less intense... or perhaps time out - organise evenings or days where your sister can have time for herself, or with family or friends while you look after her daughter. Eventually you will be able to give her the freedom of a weekend or some such offer.

I agree also with your own words, and will second Knot's statement. This is an ideal time for you to take a mental and physical break and come back refreshed and ready to help your family again.

[Zen]

When the oxygen mask drops during a flight you put it on yourself before you put it on a child.

You have to take care of yourself before you can take care of anyone else.
Good mental health and stress relief is an important aspect of a healthy life.