Why can the pony not be lunged as exercise for a couple of weeks, then reevaluate the fit of the saddle?
If doesn't matter how good the pony is, if the saddle doesn't fit and is slipping to the side, it is dangerous. The pony could be a saint and stop happily with you swinging around under its belly, but it is still dangerous!
If you put more weight on one stirrup, then yes you need to learn to have a more balanced seat, BUT in a saddle that slips sideways, this is impossible. As soon as it starts to slide even slightly off centre, your balance will be off and then it's just a circle of unbalance until the saddle is forced so sideways that it slips right around.
Anebel is right, get some weight off the pony so it is not so round, and get the saddle refitted properly - not a quick look at it and deciding it'll do.
What happens if the saddle slips around under the horse and you get stuck in it? Yes, I have seen it happen to a child on a pony and she ended up being knocked unconscious. Not nice.
Get it fixed.