Yeah fun rides are quite the flash point for a lot of horses to be a lot more lively than usual, combination of being away from home, unfamiliar sights and smells, opportunities for gallops and jumps in a big group, lots of other horses around and sometimes overtaking them or disappearing out of sight - quite a challenge for any green horse or nervous rider!
With the benefit of hindsight it does sound like it was maybe a bit too much too soon for you as a combination especially with the issue with her bridle - but on the plus side you sat the rear and didn't fall off (sounds as though maybe it was more towards the over-excited hop end of the spectrum than a panicked, unbalanced rear which are the really dangerous ones?), both you and she completed the ride albeit not together so she's had a positive experience overall and won't have ingrained it as a habit from one occasion - although some people would say 'once a rearer always a rearer' etc it doesn't sound as though you need to give up on her yet? I get that feeling of disappointment in yourself when things don't go to plan but from my experience of being an inexperienced numpty bringing on an ill-advised rescue horse, you do need to be prepared to make mistakes, have failures and learn from them as it's always a bit of a two steps forward one step back scenario IMO. So you can take some useful learning points from this e.g. perhaps you need to build up a bit more gradually to events like this one - start with quieter hacks from home with just one or two quiet companions and next time you feel ready to go 'out out', you could ask your friend to swap horses again from the start if she doesn't mind or swap halfway round the ride so your mare gets settled and the fizz out of her with more experienced confident friend on board and your nerves settle on a quieter horse too? Obviously the point about forgetting your bridle is another good learning one, to make lists of everything you need and triple check before leaving the yard (been there done that, you name the crucial item of equipment and I've forgotten to bring it!).
The thing about pulling and kicking at the same time sounds familiar too, when you're nervous and they're a bit spicy it's a natural inclination to want to hold onto their head but it's a really bad habit to get into particularly whilst using your legs as it's very confusing and frustrating for the horse - this is something I'd work on with your instructor if you can, get her to come out for a hack with you on foot or a bike if you are more nervous hacking than in the school, you need to re-programme yourself to use a half halt to get her to listen rather than just pulling and pulling, the release/'give' is as important as the 'take' - when really feeling the urge to 'hold' I put on a neckstrap and hold onto that instead, if you really feel you are being tanked off with you need to use the 'one rein' technique to emergency stop, get your instructor to demo this, hopefully if you stick to calm situations you'll never need to use it. I've also had to learn to use hacking as a schooling session with one of mine, how I would love to be able to potter along on the buckle end chatting to my friend or looking at the scenery but alas no, she needs to be worked hard for at least the first 30 mins or sometimes the whole way or she'll mess around, spook herself and then escalate into genuine fear without intervention, so that means loads and loads of transitions within the pace and up and down the paces, neck flexions, give and retake the reins, lateral work where safe to do so, lots of circles and changes of direction in any open space - she works as hard on a hack as she would in the school and this does have the side benefit of if I'm feeling a bit stressed out I don't really have time to think about it as need to concentrate on her!