I ride a horse that's lazy & sensitive. He's lazy at first but after we get going, he thinks my trot signs are canter signs. Do you have some advice?

Maybe you dont give her 100% clear signs? Do a lot of transitions and do not lose your nerve
When asking for the trot transition, make sure to keep your body back and use your half-halt while pushing him up into the transition with you leg. If you start to feel him take a canter step, use your body and half halt to bring him back; if you can sense when he is going to canter, try to be one step ahead and ready with your aids. Once you get the trot, you can exaggerate your rising and use your leg to push him up into the working trot that you want. As for the problem with the lead changes, you really have to focus on your balance. Use your inside leg and outside rein to help support him while pushing him forward with your seat. Sometimes a horse switching leads like that is just due to lack of strength in the hind end. If he is having trouble, use your aids to pick up the correct lead, keep the canter for a few steps and bring him back to the trot before he loses balance and swaps leads on you. Do lots of transitions - and as he starts to get it, start to keep the canter longer. It’s better to have him cantering correctly for a short period of time than to have him go around on the wrong lead. Eventually after time he’ll learn to carry himself and keep the lead for you. Doing lots of circling can help as well - that way you can keep him bent to the inside and help prevent the lead change. And don’t forget - reward him when he gets it right! Giving him that posative reinforcement to let him know he’s doing a good job is important and encouraging for him! Hope this helps!
maybe try slight rein pressure or half halts once you ask him to move up, also on the lead change thing, I had the same issue. if you keep the pressure even in your hands and legs, then it should help him stay consistent, it took me awhile to get it lol. on being softer, don’t be afraid to regress and do some hands-in-the-mane work once you get a consistent pace, it will help your hands quiet and you can slowly work your way up to taking them off the neck. hope this helps!
He also does lead changes when I don't even ask for it. How can I become better at holding him back from doing this and not make him jump forward into the canter when I ask for the trot or walk?
I do use a dressage whip and dressage whip only because he is a bit lazy. Also do you have any tips on leaning back and any ideas why he does the lead changes and how I can prevent/become softer? I need help!
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