@LittleLadyCece, here is another point of view for you to ponder, but obviously, if it doesn't suit you or your family's dynamics, then please just ignore me!
I would say to my 10 year old that I was suggesting she has a shower so that she feels comfortable, because Chlorine left in her hair will make it feel sticky and itchy, and she might get some spots on her skin as well, if it reacts to the harsh chlorine.
Then I would remind her that I am on holiday too, and need to be able to unwind and relax, so you are relaxing a lot of the rules that you have at home, whiich will also give her a chance to show that now she is in double figures she shouldn't need 24 hour supervision, so this is a chance for her to make some safe low level mistakes and successes for herself, as that can be a very effective learning tool. You would obviously need to let her know of any firm rules that cannot be broken OP, like just going out without asking first is not a rule that is going to be relaxed for quite a few years yet! Oh, and of course remind her that you and dad are always there if she is overly worried about something.
As for your 15 year old, explain to her quietly and gently, but also firmly, that you deserve a holiday too, and that quite frankly you don't know what has got into her. Ask her if she has fallen out with her friend over something, and if she has, see if you can help the two of them call a truce?
But whatever the outcome is to whether she and her friend are alright with each other, and if, presumably, your DD actually wanted her friend to come on holiday with you all (that you and the friend's mum hadn't concocted the idea of the friend coming on holiday with you as a way for you and friend's mum to have them out of your hair(s) for a week or two!), that your DD at 15 years old, is the one who should be acting as the main host for her friend, whilst reminding DD (that unless her friend practically lives at your home during a normal school week and the holidays) that her friend is probably feeling a little shy and awkward, as she may feel that she can't just ask you - friend's mum - or your 'in the doghouse' DH, for an ice-cream, or a soda - if allowed whilst on holiday - or she might think that she couldn't say, if she didn't feel happy at the evening's entertainment, as she was exhausted and just wanted to go to bed.
I presume that your DD's friend is 15 as well, and if so, then I think that the holiday without her family around her - but while still being in a safe place - would hopefully be a positive learning tool for her? However, I still think that all of you, but particularly you (as the mother figure) and your DD as the host, have a responsible part to play in helping the friend enjoy her holiday.
I am sure that your 2 DDs are usually lovely, but they are both old enough now to be influenced by 'outside of the family events' which may start having more of an impact on them, and as you are all growing out of the encompassing and protective bubble that most of us probably live in while away with our young children, this holiday might turn out to be more of a catalyst than anyone expected. If everyone could try to "chill-out" a little more, that would hopefully help quite a lot, and if you and DH could come to an agreement that on alternate day/nights, you can each have an hour or two to yourselves (ie. It's your turn tomorrow evening), that might give you both a little boost as something to look forward to after a day of having 'fun' altogether!
I really hope that everything has settled down by now OP (this has taken me ages to type on my phone's keyboard, in fact your whole holiday might be over by now!), and that you are all having a great time xxx