I imagine that this is frustrating when you receive pressure from others. Parents can influence a child's choice to use the toilet, but it remains THE CHILD'S CHOICE. The trick for you is to find the best way to motivate your daughter.
Since your daughter will go for the grandmothers, it sounds like a control issue between you and her. Don't give her opportunities to make it a power struggle. Skip the "big girl" panties and stickers to reward her. Treat the toilet use as you would using a fork or drinking from a cup; it's an expectation.
If I was in your position, I would simplify the situation. Put her in diapers all day. No pull-ups. Explain that she will be in diapers until she can put all the poop and pee in the potty. When she goes in her diaper, don't be too quick to clean her up. I don't mean letting her sit in it for a half hour, but 5 minutes of waiting isn't unreasonable. Plus, it will give you a moment to focus on being completely poker-faced about having to change her diaper... don't give in to frustration or even thoughts about "why won't she go in the potty?!?!?" She's at the diaper stage, that's as simple as it is. You can use language like, "Does that feel gross in your diaper? If you put the poop in the potty, it would feel so much better for you." Or if she comes into the bathroom when you are going, say, "See, I wear underwear because I use the toilet. Grandma So-and-so uses the toilet, too." Be matter-of-fact, do not patronize her for her choice.
Skip the "if you do this, then you get this" talk. You cannot motivate her to use the toilet with things. Keep stickers as a last resort for when she is closer to being fully trained (i.e. pooping more regularly in the toilet, or staying dry overnight).
Alright, so assuming that you are putting her in diapers all the time, meet up with her friends that use the potty. She's aware enough of her environment to notice that so-and-so is the same age and using the toilet. This may be the very thing to close the deal for her.
Please know that my brother was at his wits end with his 3 and a half year old. I flew out to visit for a week, and trained my nephew. He would go for me because it wasn't about control. You may need to enlist the help of a friend or family member if things don't change before the summer. I hear you about the pressure of preschool enrollment. I wish you all the best!