I do the circles, weave around the trees, lateral work, etc. too. But as I trail ride, I try to make sure the horse will always walk coming home. Sometimes it takes a lot of riding and time, but I try to get them into a calm state of mind before we head back.
My new mare, for instance, I got in the middle of winter, and she was hyper as all get-out. So rode her up and down hills in a really hilly area of the forest until I could point her towards home and she would walk. Then I tried to always give her loose rein. Sometimes she would get nervous or hyper again and I would have to tap the breaks, so to speak, but mainly they seem to stay calmer on a loose rein.
I don't know if your friend's horse refuses to walk, or expresses it's nervousness in other ways, but that is what I do if they are too worked up to walk home. Lots and lots of exercise. A tired horse is usually a calm horse.
If I want to canter or do faster work, I try to do that going away from home. Try to burn off the jet fuel on the way out, lol, and then work on walking on the way back when hopefully much of that energy is gone. Sometimes you can get so frustrated and the horse wants to jig all the way home, and you just can't win. But don't give up because often the next ride they behave like a different horse. It might even take a few rides to get that worked out of them, but with enough release of energy, eventually you should find the calm horse inside. Kind of like shaking up a bottle of soda, and you have to release the pressure in a controlled way until enough of the pressure is gone and they you can open the bottle.
Also, they like to learn routines. So if you always canter in a certain place, then the horse will get hyped up in that place in anticipation of the canter. So I try to keep them guessing and never always do my fast work in the same place. I may have a favorite cantering spot, but I will have them walk on that section of trail more than I canter it.
Anyway, I really don't know the details of your friend's horse's behavior, so I am making a lot of suppositions. But maybe some of it will be of help.