As chunky monkey says one cant tell whether it is you or the horse.
Part depends on shape of horse. Marnie was narrow shouldered so her saddle tended to slip.
Plus a soft hearted rider may not tighten the girth sufficiently. I was taught always to check my girth after riding as couple of hundred yards as on my old share it usually needed tightening. I was taught how to do this from the saddle at one of my first lessons but as I grew older, it is something I now avoid.
Then there is old people being more crooked. May be down to your spine (as it is with me) but some people it is their hips.
My weight is always to the right. So I know always to check that any saddle is central on the horse and that it stays central as I ride. The odd thing is that my current share the saddle does not slip - I havent got any younger so it must relate to the shape of the horse.
In the school I was taught always to alternate the rein (i.e. direction of travel.) Because any problem from crooked horse or crooked rider is likely to be worse in one direction than in the other. Both horse and I were worse on the left rein. I need to remember always to keep my outside (right) shoulder back. And my left knee down. At least doing that might help you in one direction.
On the right rein the saddle may be slipping to the right while you are on the straight but you dont notice it. That happens to me out hacking.
Opinion seems to vary from one RI to another about whether or not the horse should be kept vertical going round the corner of a school. I recently had a teacher who was insistent on that. However our regular and senior teacher never mentioned that at all. But she did always describe two other things. First that as the horse goes round a corner or curve you imagine two railway lines. The outside of the horse travels further than the inside. And she also spoke about riding the whole length of the horse. From nose to tail. We learned this partly by riding with counter bend. If you think about "riding" the horse, I find one is less likely to slip.
I dont know the age of the horse you are riding -Our RI and Rashid both describe school work like going to the gymn. It is not something one must over do. Introduce the horse to anything new very gradually and over several days or weeks. But at that RS the whole emphasis was on bend and turns - the horses were trained to go straight out hacking when they were young but for the mature lesson horses and liveries the bending and suppleness was what mattered. We warmed up in walk only and with many turns. I never encountered that at normal riding schools.
But any problem with corners is a problem with suppleness and turning. If your horses are used mainly for hacking they may find corners an effort. One could help them by making the corners more shallow ie leaving the straight side earlier and returning to the straight side later.
I have not ridden since March so I really worry about not being able to get on and off the horse. But I have found that everything is much easier following an escort. If you followed your daughter round the school just having her vertical young body in front of you, and needing to use less leg on a following horse, might help you not to slip to the right.
Apart from riding, my daughter seems to think that stretching is very important as one gets older . The Jo Wicks senior exercises OH and I have been doing in lock down seem to improve that stretching without demanding much effort. Each of us knows their own body. The difficulty is that you say you have a problem, So if it is to be solved, there must be some change made. But what is possible for you and what is not, only you can know.
I know my problem is not getting up and getting dressed.