If you feel your lower back muscles are failing you, then do some exercises - see if you can find a Pilates instructor. If you are new to riding then it will take time to acquire centre core muscles.
Watch the horse in trot - slow the film down - understand the way the force is generated and how it can be absorbed.
Note, your spine cannot absorb force - it is your toes, your ankles, knees lower thighs and hips which absorb the stresses created by a trotting horse with a little help from the flesh of your butt. But your brain has to learn how to retain balance whilst absorbing the thrusts. It takes time.
Find a nice broad backed cob with a naturally slow but rythmic pace to practice on.