This is getting utterly ridiculous? Really? Why would a sibling worry and state their worries about their Mom being alone when they'll do almost zero to help? I'm not going to live in this tiny little shell so Mom can be comfy. If she wants assistance or help or to not be alone, I'm not the one for her! Help!
Realistically, what are the risks to Mother being on her own for a few hours? For a few days?
If you got into this without intending to be on-call 24/7 but that is what it is turning out to be, maybe it is time to get out of this, and make sure Mother is well cared for in a different setting.
What solution do your siblings suggest for not wanting Mother alone and yet Mother living where there are not 3 shifts of trained workers to attend to her? What do they want to see happen? (If the answer is "for you to stay home 24/7 and be with her" disregard their input totally, and make decisions on your own.)
AFTER vacation, start looking into other suitable housing options for your mother. Realize that you cannot insist that she goes to a particular place of your choosing, but you certainly can insist that she leaves your house. Helping her find another place to live is just a courtesy on your part. If she wants to do that on her own, that is OK, too. Or maybe she'd like to have her other children help her with that.
One step at a time. Vacation first!
Can you arrange for your siblings to call her once a day while you're gone? How about calling neighbors and asking them to stop in? You can call once a day to chat.