Sorry to hear that you are struggling.
It sounds like you are frequently experiencing what are called subluxations of your knee cap. There are a lot of things that can be done to help you.
How did your appointment go at Nottingham QMC ?
Keeping your leg immobile for that long is not a good idea as the muscles will weaken.
Have you recently have any physiotherapy ? Seeing someone that has a good understanding of these problems is really important. It is important not to just strengthen your quad muscles, but also your hamstrings and glute muscles too. Over the years I have had quite a few physios give up on me, but then I had some great physios that were excellent, knew what they were doing and closely liaised with my knee surgeon.
Make sure that if you decide to go ahead with surgery it is for the right reasons. Also ensure that the surgeon you specialises in patella problems. The most appropriate types of scans for patella problems are CT scans and plain x-rays. MRIs are useless unless they are looking at the cartilage surfaces.
With hypermobility syndrome it is really important to do some sort of regular exercise. The exercise should be gentle and low impact. Things like swimming, hydrotherapy, clinical pilates and a gentle gym program can all be good. Sometimes walking is an option, but not always.
As for your daughter I would suggest taking her to see a paediatric physiotherapist.
I hope all these ideas all help you. Let us know how you are going.