My old horse did the exact same we tried crops spurs etc did not help at all if anything it made him worse so we got our vet out and our saddlery fitter and nothing wrong with that we then got our farrier and he had some hoof issues so that could be the issue but I would not start with a crop or spurs as that is 1. Slightly cruel if it turns out the horse not being lazy and being it pain so you would be punishing her for being in pain and 2. Crops and spurs should be a last resort and finally 3. If it is incorrect use of them the you could potentially ruin all bonding you have done with her through grooming and such
Hope this helps
You can always try a whip or spurs my favourite is a dressage length whip so i can encourage from behind. But just in case have her back checked and make sure your saddle fits correctly.
You can also look into getting your horse chiropractord. My horse gets her back done and it seems to help her a lot.
Does she do this on the lunge? If she doesn’t have that problem on the lunge then it may be a behavioral issue. If she still doesn’t trot, hen it could be either a behavioral or health issue. You can also try to see if she will trot with you leading her (just halter and lead) to see if she will trot. Good luck!
What does your instructor say? They’re the best source of help. It could be anything from a physical issue to a training one.
My pony is very lazy. I would try using a crop if that doesn’t help. With the crop hit him/ her on the behind she might buck or kick but you need to prove to him/ her that you are the boss of them.