Phly, I don't think the OP put his/her opinion on it. Just that of his daughter and partner.
I agree with Sorrell, (she didn't say to do this) but just make sure you keep smacks away from the face! That will create a head shy/nervous horse.
If my pony is having a day where she thinks she can push me around and a small smack on the shoulder doesn't work, I lean into her with my elbow and make it as uncomfortable as possible. If the pony finds it uncomfortable/painful he'll stop.
As for the lowering of the head, teach the pony how to lift/lower his head from pressure. There are lots of videos on it but its a really simple task, just takes a little time.
To lower the head put pressure on the poll area with your hand, and as soon as you get even the smallest reaction release and give the horse a pet/rub. Repeat this again, each time making him drop his head a little more until he feels the pressure and thinks "I should put my head down". Don't make this a frustrating experience, spend 10 or 15 minutes on it a day and move on until he gets it.
To raise the head, do the same thing but pull up with the lead rope, don't yank it, just put a steady pressure. This helps too when he will decide he wants a bite of grass.
The key to this is to make sure you reward the horse with release of pressure, a good tone of voice and pets/rubs.
You may want to show your partner this thread, so she can understand why
its not going to hurt the horse.