You mean I'm not supposed to carry that bag of M&Ms in my saddle bag?
I would forget about addressing this with reins. Anytime she starts to grass dive, give her a kick and send her forward. Unless she's very talented, she can't eat and walk at the same time. She needs to know this is 100% enforceable and she is not allowed to do it. Make sure to reward her with release of pressure when she does give you what you ask for.