You don't say if you've had any consultations with rheumatologists; x-rays, any other screening just to make sure we are dealing with a postural problem with joint laxity rather than an on going "sub clinical" inflammatory condition. Not that I want to scare you but all that stuff is useful just to know it's, as far as one can tell at present, nothing serious. Do you do any serious/less serious sport? General fitness? Weight +/- height+ -?
As has been said, we have to live optimal posture in everday life and reprogramm our posture as just doing the core stability and still slouching doesn't work. Despite being a physio of many years I'm going to suggest you head in the direction of Alexander Technique to help your postural awareness and help your back problems. Most physios will suffer back pain at some stage in their working lives. It's a tough profession to follow. A friend of mine went through a really bad spell and as a physio, we tend to go to a physio, sounds OK! But when it doesn't help as much? where then? My friend discovered Alexander, and to cut a long story short ended up qualifying in Alexander Technique too. Back pain relief included. Now she has a different approach to postural pain issues which "physio only" practitioners can benefit from too. If you want more information let me know, my contact is n Derbyshire but will know other double qualified physio/Alexander-people.