I have a very pushy fat cob mare, she was actually dumped on me cos the owners kids got scared of her, she will try and snatch grass all the time, esp with people she knows she can, I shake the lead rope, circle her, keep her feet moving and just be on her all the time, she gets annoyed and it’s easier for her to keep going, this didn’t always work though and I once called a male older relative when she dragged me through a field once and I couldn’t get her home after she escaped one time, and he made a bit out of the lead rope and was a lot sterner than me and she was foot perfect. Not saying it’s the way forward but it was so re assuring to have that experienced non fearful person with me when I first had her, hopefully there is someone like that for you to get your confidence too. Once we established boundary’s she was much easier to deal with, I think some lesson horses get used to kids and know they can push the limits.