How do I get my sisters to help?

I say call your sister and tell her you want to take her up on her offer. Leave her a list of instructions and take a vacation to reboot.
I will be taking Mother home for a few weeks soon and my brother plans on visiting for a week. I'm going to disappear for a few days so he can have some "bonding" time.
Take what you can get. It might shed some light on what your situation is like.

You aren't wrong if that's really the way you feel but I would urge you to give it some thought. While their reasons may not be as thoughtful, your sisters reluctance to take your aunt to their houses for a visit might be smart. At 93 especially with any kind of dementia spending 1 night in a different place never mind a few or a week or a month can be very hard and can have negative effects that can be very hard to re-balance even after getting home. If she has been living with you for a while taking them up on coming into your home because it's her home really might be the better idea. If aunt doesn't have to change what's familiar, keep the same routine, it will be far easier on everyone. Consider taking your sister up on her offer and you go away, take a little vacation and or simply check out of the care giving, come and go as you please and live in your own home unencumbered by your aunts needs and schedule for a while because your sister is covering that. Go ahead and veg out in your own house and let whats going on around you be someone else's responsibility for a while. They are offering do what you need to to take them up on it and don't turn it down simply because it isn't offered the way you picture it or want. You are just shooting yourself in the foot by doing that, take the break however you can get it! That said it is up to you, you aren't wrong for saying no but you might not be making the best of an opportunity all be it a less than ideal one.

Yup, youre right. I take "care" of my aunt. She is in a facility so, I have her 2 minutes away from me. Tag, I am it. Nobody else to visit her, buy her the toiletries she needs etc.
You are more hands on. That is a lot. When my friend's sis retired, friend said, Good, now it's your turn to take care of Mom! What would they do, if you dropped auntie off at their house for the weekend? Or are they too far away for you and aunt to drive to their homes?