Have you looked into Clicker Training? As previous posts have suggested, it's entirely positive reinforcement. When she picks up her foot on cue, *click* [this is after teaching that *click* = right and right = treat]. It will help her clue into what good behaviour you are rewarding her for.
Touch her all over. Including under her tail. If you ever needed to take her temperature or anything included of that area. This means inner flanks and teats too. Play with her muzzle. With enough time, she'll bond to you as the Boss Mare; probably replacing you as a surrogate human mother. Make sure when leading that if you stop, she stops. End.
I taught my yearling 'hand'. If I ever feel that she is too close/too far in proximity or even not paying attention, it's "Hand" and she walks up and touches it. IME, this is useful for her leading beside me, not behind me.
A common practice for us is: "Walk on. Whoa. Back. Back. Whoa. Walk on. Hand. Good girl." [strewn with 'good girl'] -- The point is that at all times, I control her feet.*
Also, another side note.. One Horse Year = 3 Human Years in mentality; [Yearling would have mentality of preschooler, etc.] and that soft hands make soft horses. Make the right thing easy and the wrong thing hard. Discipline bad behaviour and refine good behaviour. If you know she can do it better and faster, with time, then don't settle for half-hearted efforts. I think you'll do great with your foal! :)