I started aged 62. I got almost nowhere with riding for the first 9 months - and during that time I had a 6 week gap after breaking my ankle walking a coastal path.
In the long run it doesnt matter.
But some questions. Is a conventional riding school the best place for an older beginner? I was bullied by my first RI. (and rescued by NR) No one should be crying after their lessons. So ask if you are being treated nicely by your teacher and well taught.
Next - new riders often get fobbed off with many different teachers - are you getting continuity and is your teacher/horse right for you?
Many schools keep a strong cob for beginner adults but old people may not be able to sit straight astride a wider horse. I was constantly blamed for sitting askew, but they had given me the wrong horse.
Understand that a riding student is not tied to one school. Take a break or find another place? I changed to another (less highly regarded) school after a year and everything was different.
Understand that at some schools even beginners can hack out or you could go for a trail ride.
In my first pointless year I none the less learned some valuable things.
I learned how to lead a horse in and out of the stable and how to untack him and put on a rug. Learning to lead a horse and have him do as you say may come easier to an older adult than controlling him when one is sitting on his back. I do recommend a couple of lessons in grooming, tacking up etc and then perhaps volunteering to help.
I learned how to groom and to pick up the feet and clean them. Very important lesson.
Grooming and leading the horse established a bond between us. He was my ally against the horrid teacher. Years of watching David Attenborough teaches one a bit about animal behaviour.
But combine this with saddle time however depressing it seems. My OH always said that what mattered most was saddle time. Give your body and mind long enough and anyone will ride. He started aged 67.
Your relationship with horses is in the end going to be more important than any of the technicalities of riding. For the riding and for staying safe and balanced in the saddle nothing is better than lunge lessons. Lunge lessons are stress free and safe.
If you cant make the horse trot - forget that moment when you ask. Think for a bit about getting the horse ready to trot. It is how you ride the horse in walk, just before you ask for trot that will make all the difference. Imagine you are dawdling up the street and someone suddenly shouts at you to start skipping. One needs a bit of warning. The horse needs to be ready too. One way even a beginner can get a horse to move off more easily is to ride several halt walk transitions. The same with trot. Trot six steps, walk six and then trot again. The horse is a living creature with a brain. You are planting the idea in his head. As you ask, reduce the strength of your cue. The horse will appreciate that and will become more sensitive to the lighter signal. The changing from walk to halt or walk to trot is called a transition. If the horse isnt moving for you, ask the RI if you can ride a few transitions. The RI will probably say yes.
A major problem for us adult beginners is that we are used to being obedient to a teacher and we try too hard. We put more and more physical effort into the riding when we are corrected and the horse seems to ignore us. To ride well one needs to do the opposite - breathe deep, relax, be gentle, coax and coach the horse.
The great rider Charles Harris when given a horse to ride would mount and then just sit there, relaxed and allowing the horse to relax too. The trainer Mark Rashid recommends the same. The moment you sit in the saddle, both you and the horse are likely to be tense. The horse has your weight on his back and the rider is less secure since his feet are no longer on the ground. So just wait in the saddle for your horse to relax, for the head to lower. Give yourself a minute or two. And then when you are both relaxed , give a little touch to one rein - that will signal to the horse that you are now going to ask him to move forward. Then ask. Politely. You have achieved something already. You have had a little conversation with the horse.