Using an arctifial aid like a crop can be vital when you don't have the leg strength to ask them to do what you want properly. Don't be shy using a whip if you need it but rather than hitting them repeatedly, ask "nicely" with you leg, give them a light tap behind him your leg, and if they don't respond bring it down hard on their butt (NOT on the shoulder). Always ask with your leg first, and follow up strongly with the whip if necessary.
Using a crop isn't a bad thing. If you think about it, horses are much bigger than you. Using a crop DOES NOT hurt them. Have you seen how they fight in the pasture? If anything it just makes them feel uncomfortable so they will do what you ask. They find it more annoying than anything, that's how my horse acts anyway when I smack her. If you don't kick and smack with a problem horse, it could put your life in danger.
You should really listen to your train and hit the horse even if it's a light tap on the shoulder or a small kick because if you don't kick or hit they can learn bad habits. But if your trainer is constantly saying hit or kick the horse train with a trainer that says to cluck or squeeze more of
I would say bring the whip but that doesn't mean you have to hit the horse. A whip should be an extension of your arm or leg and should only be used for tapping the horse mainly. If you are repeatedly being told to hit the horse tell your trainer your not ok with hitting him. Then if things don't change get a new trainer
If you're told to constantly kick the horse, it doesn't seem like he's good on your leg. A crop can help. A lot of horses react faster in the leg when they know the rider has a crop in their hands, you don't even have to use it.
My first barn would tell me to kick but also when I was there my feet wouldn't even come off the saddle so I didn't have much leg on anyways. The new barn that I went to told me to smack this one horse with a crop really hard and that was the last draw for me. With my horses I squeeze with my lower leg and they listen. I carry a crop with my older horse because he needs a little push but I NEVER smack him with it. I literally give a light tap or even just putting the crop up to his hip helps.
Just because your carrying a whip, doesn't mean that your going to be constantly hitting the horse, some horses just need a light tap, or just to see the whip, and then they will be more responsive. If your trainer is telling you to wack the horse repeatedly, then maybe it's time to switch barns.
*ride. Should I move barns?