I agree with GTD. Make sure the horse’s hind footprint is falling into the front print. If it is, this is probably the walk the horse has. If not, then you can do some urging.
When you are whacking with the crop and kicking constantly, you tense up your whole body and your breathing is eratic. Instead try to learn where each hind leg is in the sequence of the gait. A person on the ground will help calling “left - right - left right.” You can ONLY influence each hind leg when the leg is off the ground. When the person calls left, that means the left hind is airborne. Let your left leg and hip swing and squeeze from your crotch to your knee during the flight phase of that hind leg. Same for the right. Learn to feel this rhythm. Breathe in and out, steadily and deeply. Any kind of tension blocks energy from your horse’s hindquarters into his body.
It takes an hour session of this in an arena or on the circle in the field to learn this rhythm.
Of course if the horse is downright sleeping and totally ignoring your seat and leg, haul off and WHACK once with the whip (I would use a 34" stiff dressage whip). Make it sting and leave a whelt if necessary. Don’t just pester pester pester, tappy poo tappy poo. Reach up and grab some mane and hit that bastard like he just attacked your first born child. I mean it. There is NO EXCUSE EVER for ignoring your aids and cues. EVER. It is dangerous, sloppy, and completely unacceptable. It takes 1 or 2 serious whacks to leave a mark and a sting and the horse usually wakes up and KNOWS you mean business. (But of course always give the horse the opportunity to give you the right answer FIRST before going to the whip. Ask once, ask twice - go to the whip.) Sounds like yahoo giddy up cowboy but it works. I had to do it to a dressage horse of mine years ago. This is a tactic I learned from a dresage trainer.
Then you go back to your calm, tactful riding, slow breathing, creating and allowing energy to flow from the hindquarters, open pelvis and swinging hips. If you pester and tappy tapp tappy poo with that crop, after a while it’s just white noise. Horse tunes it out. You kick kick kick kick and nothing ever changes.
On another note, I had to train my horse to trot and walk. She wants to just canter canter canter all the time. By riding her with experienced endurance horses, she has learned from them simply by watching. She used to canter canter canter mile after mile when all other horses were trotting. She could canter at another horse’s extended walk. Just by getting more miles and experience, and putting her neck to neck with experienced trail goers, she started matching their gait and speed. Sure, I work on her when I’m alone too, of course. But she just “gets it” SO MUCH easier when she’s with experienced horses.
I combine the experience of other hroses with my own loose hips, open pelvis angle, relaxed breathing, and combination of leg and rein aids.