Just introducing myself. Recently got back into riding as an adult after 10 years off & discovered that I'm like a sack of potatoes in the saddle! It's certainly not like riding a bike
Your core strength has gone, but it will return with time in the saddle, then your body will start doing what your brain tells it to and everything will fall into place. If you want to get fitter quicker it helps to do other exercise as well, eg cycling is good for strengthening the legs and pilates is good for your core.
Welcome! How about a couple of lunge lessons as well, which will help you concentrate on you instead of the horse. You may find some of your issues just need a tweak in posture/position to be resolved. Good luck.
Thanks nikicb, that's also a good idea as I find it hard to concentrate on me and the horse all at once. I did try other sports during the long break but riding was the one sport that has always given me a buzz; trust me to pick a mega-expensive hobby!