If she starts to drag, turn - into her so she has to turn maybe. Don't go in a straight line all the time, that will also slow Bay's walk down just a bit. And please be careful - she sounds like she'll be okay but we've had horses, generally the babies try to rear up or bite since their head is right at your knee.
I've been pawed at by babies ponying momma. I don't fear her doing that. She has never done one aggressive thing, even when she's in full panic. She misbehaves, but usually just trying to get away.
It might make for a comical set of pics if we do get the gumption up to try this again. If she would come with us, she'd be a good pack pony. ;~D