Another thing you might want to try is to get her trotting in a circle on a lunge line since she knows how to do that already, then turn and go with her in a straight line and keep encourageing her to trot.
That's the way I thought of starting my pony at it, was as a lunging trot where the line just kept getting shorter ;~D. She's not lazy... she trots everywhere in the pasture simply because it's a quicker way of getting around. She's got some kind of mental block. If you try to get her to trot in hand she just plants all four feet.
Lately I lead her without the rope. Not today. She just wanted to eat grass and at a slow pace she could try to grab a bite. I have no trouble getting her to trop on the lunge line. I have to get behind her butt to get her to lope sometimes though. The circle interesting. I'll try that. I really don't want my husband helping. I love him dearly but....:')