What you've described with Rainbow is something I experienced with most of my 7 horses, so it's not uncommon and it will improve as you find what works best for each horse. Your post brought back a lot of fond memories for me.
When my first 2 minis appeared about 8 years ago, my horse-experienced neighbor came over literally every day to hold the lead on each horse while I learned to pick up their feet and clean them. My neighbor had previously been a farrier, and she assertively insisted that I clean hooves every day no matter what. I am eternally grateful to her, since cleaning hooves was one of the many things I didn't know about horses at that point. Having a header who keeps the horse from moving far, repetition, patience, and consistently rewarding the desired behavior helped me work with the horses' hooves.
I'm not an expert by any means, but now my horses are pretty cooperative when the farrier, my husband, the vet, or I inspect or clean their hooves. As soon as I set down the finished hoof, they will lightly lift the next leg anticipating which hoof will be next.
Starting at the shoulder or at the hip, slide your hand down the leg, lifting a hoof, holding it up a few inches for two seconds and setting it right back down. If the horse stands still for those two seconds, reward it greatly. Repeat on the same hoof, and give a reward (lots of praise, scratches, a treat, whatever). Make the sessions very short so there's a chance for success. Be patient and don't expect too much all at once. One leg a day may be fine for a few days. Gradually increase the number of legs until you've been successful with all of them. Start on different legs on different days, too. The "leg of impatience" might improve if it has attention first, shorter sessions, and more praise.
Next, clean the hoof lightly with the pick for perhaps five seconds, then set the hoof down. Keep the time short, and the hoof not too high off the ground. Reward profusely. Repeat with the same hoof. The purpose is for the horse to learn that lifting the hoof and feeling slight pressure doesn't have to be uncomfortable or result in a game of fight/flight. As with other horse lessons, it's best to stop on a successful note. You can always add another hoof the next time. Continue to the other hooves gradually. Again, be patient. One hoof may be the limit during each session at first. Three hooves might be successful next week, and perhaps all the hooves by the third or fourth week.
Rainbow might improve as you work with her frequently in shorter sessions and the more you reward her for her tiny successes. Especially with Rainbow and the foal, I would have a header there as often as possible. A little experimentation might help you discover what works best for each horse. For example, one of my horses relaxed much better if he could eat from his manger when we started his hoof lessons. Another horse was less antsy if I walked him a little after working on each hoof. A couple of them stood more patiently when another horse was tied next to them during the beginning lessons. And standing next to a wall helped a horse or two not move around so much. They all still seem to relax best If I brush them first, with the hooves the last step in their grooming routine.
In the past, my horse, Sandy, enjoyed leaning into me heavily when I picked his hooves, but if I moved away, he lost his balance, making him stop leaning on me. I immediately resumed working on the same hoof as if nothing had happened. I don't know if that's wrong or right, but it stopped the behavior.
Repetition, consistency, patience, and a header combined to make this a success for me and my horses. I hope this helps you a little.
Pam