If you already know you have weaknesses, I would really, really encourage you to have some private lessons, alongside, not instead of the weekly lessons. Pilates , yoga, well anything done well will be very good for you, its very easy, though, while you are learning, to do it wrong. You know the next day, because your muscles don't hurt and perhaps your back does.
Many teachers will say they are looking out for the class and won,t let you do things incorrectly. Its not so easy, though, to see what is happening inside. There is no way to say in advance how many privates you will need. Im ashamed to say it took me a year, and lots of other things falling into place, before i stopped hurting my back and started doing the exercises correctly. Once you feel it, its easy enough to notice when you do it incorrectly and gradually it will become second nature.
Teachers tend to prefer group lessons ( ten (or more) people ten pounds each compared to a single person paying, they will always get paid better for groups. Any teacher who is interested in doing it correctly may well be prepared to do some privates. All the best, it was quite magical once i got the hang of doing it correctly. Back never hurts now, so long as i keep up the exercise.