That's great that your mare has an awesome trot. There are a couple of different strategies for strengthening her back muscles for the sitting trot:
1. At the posting trot, make sure she's really working and pushing from her hind end and that the energy you create with her hind end moves forward over her back so that she stretches forward with her head and neck into a soft contact. If you find that you have to pull on her mouth to get her to round into a frame, then chances are she isn't working her back muscles properly. You can make sure she's working from behind and improve that quality by riding many transitions (walk/trot, trot/canter, walk/halt, trot/walk and canter/trot) while maintaining a soft contact. The transitions will help her engage her hind end more, which in turn will strengthen her back.
2. To help gradually strengthen her back muscles for the sitting trot and get her used to it, work at the posting trot on a circle, then sit for three beats, then start posting again. Do this several times around a circle. When you feel she maintains a good trot while sitting for three beats, gradually increase the number of beats you sit.
3. Walk and trot up and down hills, even if they're only slight, which will help her bend her hind legs more, strengthening them as well as her back muscles.
4. Walking and trotting over cavalletti is another good way to strenghen a horse's hind end and back muscles because she has to lift her hind legs to go over them. You can start by walking her over one pole. If your horse accepts this calmly, then set a second pole at a distance of 2-feet 8-inches to 3-feet 3 inches apart. (Experiment with your mare's stride length until she's walking over them comfortably, having to reach just a little, but she isn't putting in an extra step.) Continue adding poles, until you are walking over a maximum of six poles. Repeat this at the trot, setting the poles at a distance of 4-feet 3-inches to 4-feet 10-inches.
I hope this helps. Good luck!