My guess is that the western saddle does not fit your mare. The slipping, even when cinched very tight, is a big indicator that the fit is not right. It could be the tree size or shape, it could be the rigging position, etc.
Pics of your mare wearing her saddle would help us to see (as much as is possible in a photo over the internet
) more definitively and specifically what the fit issue is. Pics should be of your mare standing square, straight on from each side, from front to back (showing the shoulders and gullet) and from back to front. For the pics, the saddle should just be setting on her back, no pad and no cinch. Also, a look at the underside of her western saddle pad after a ride can tell an interesting story about her experience in terms of sweat marks and wear patterns.
The only fix is really to find a different saddle that fits her better. If your trainer's saddle does better, try taking some photos to compare it to your saddle and see what the specific differences are between the two. If you can find out the dimensions and specs on the trainer's saddle, that can be a great starting point in finding a better fit for her at home.