what would concern me, is that if you are right, and you going is bothering her, and so you stay - the message this sends is that she can get you to do what she wants; and that, instead of deeloping coping mechanisms herself, she is relying on you "making it all better" - which you cannot do, all the time, forever.
is there a compromise that you can come to? ie go away, but call her every day at a set time to go through her day/talk about anything that has bothered her? is skype a possibility?
if you did stay, hypothetically, what woudl you be doing for her that her dad, or her sister cannot do? why would she be happier if it was you, rather than them?
has she been upset over it in previous years? how did she/you/your dh and other dd cope with that?
sorry, lots of questions, but the anwer to how to deal with this may lie in the answers to those questions.
equally, thoguh, you need to consider - if you go, and come back early because she is not coping, same message is given. so any compromise needs to be agreed before you go, rather than "in the moment" once you are away, iyswim?
Like all those kids who cry when being dropped off at nursery, cry when their parents pick them up - and are absolutely fine in between.
And if she isn't fine - it's a good growth experience for her. She is old enough now to start taking some responsibility for herself (She's 13 isn't she?). She needs to gain some independence. You can't be there for her forever - because it's not good for her.
Plus of course if you don't have enough charge in your batteries, you can' be there for here the rest of the year......
I would say go... (I am off in Oct, for 4 nights) I did it last 2 years and it was amazing, just to be alone, it was lovely...
(had to do all the arranging of care, support and transport for ds and dh, preparing of meals, ringing home each day, and did come back early first time as ds was ill and dh was concerned) but def def worth it...
Seriously. Go, and switch off as much as you can. This is what this break is for. As a PP said - if you don't get this break, you will not be as much use to her anyway over the next few months, as you will not have had a chance to recharge.
It is hard. But it is worth it - both for you to have a break, and to prove to your dd she can manage without you.
I have only done it once for any length of time - 3 nights away at a conference last year. dh was also away for 2 of those nights, and the girls (then 6 and 3) were looked after by a new nanny - she had only been with us for 3 weeks! Unsettled was not the word (me, not them!).
BUt they lived, and enjoyed themselves, and it was all ok (dd1 usually has to be surgically removed from me, such is her dependence). And despite the worry I had (and the constant obsessive phone checking), it was a good break for me too. Just being away makes all the difference, even if you do take a proportion of the stress with you!