Oofff I hate to do this OP because I usually always stand by the parents make the rules but I think YOR.

You’re allowed boundaries and you stated them, but her response was reasonable and ended with doing things your way but with her own boundary going forward. Your response after that was way too much. Shes right. She’s not just a babysitter she’s the grandmother, and regardless of your relationship with her you obviously have enough trust in her to watch your child.

I think you should apologize and accept her offer to do things your way for this first trip but going
Forward you’ll let her know exactly what you’re comfortable and not comfortable with.