In addition, I would stress that your parents need the consent of all those with PR to take your 14yo out of the UK and if you don't wish to consent then they would need to the expense and trouble of trying to obtain a court order (which they would find difficult to apply for as they themselves don't have PR).
I would take some time to sit down with your daughter and explain that you not agreeing to her going is nothing to do with you not wanting her to enjoy a holiday abroad with her grandparents and aunt, but that you feel that it's dueto granny being unwell, and that as aunt and bf aren't even staying at the same hotel, you are concerned that daughter won't be looked after properly. I bet right now, all daughter hears is that you are being a fun-sucker stopping her from having a lovely holiday in the sun and she needs to know the real reason why you've said "not this time" (I would leave out the stuff about your parents being controlling and your sister badmouthing you - keep it focused on your daughter)
Thanks for your reply. How do I put a stop to this bad mouthing? Is there anything I can do legally? My other 3 children have seen through it but at 14 my youngest is involved with discussions about me by judgemental and controlling adults who should know better. Putting a stop to seeing these family members will only cause more upset for her but I have started to log some things she is repeating and I am concerned. I just cannot understand why anyone would want to cause damage between us. Bringing up teenagers is hard enough without all of this. Thanks