I'm very confused. I see nothing wrong with him grabbing her waist. I suggest she was startled and doesn't know him. My response would've been to give her a hug, tell her she's OK and suggest she go back to playing. If she wants to stay, I'd let her stay. She was OK, right? You trust her grandfather to not purposely hurt her.
She's 3. Because she's young and inexperience, she's socially awkward. Having him grab her is your opportunity to teach her that her grandfather didn't mean to scare her. This is how you help her learn about her family. This is the beginning of her learning to have trust in her world.ie; her family. If she's afraid of her grandfather, that is.
I suggest she was startled, and as all children this age would do, go to Mom for help handling her emotions. I suggest that your negative reaction increased her fear. "Mom's upset. There is something wrong." Without your help, she will be wary of Grandfather.
Why would you keep her away from family? Family is the safe place for children to learn about people. Sounds like she has spent very little time with her grandfather. Sounds like you're uncomfortable with his social awkwardness. Lots of people are socially awkward. That's OK. I suggest you find a way to show love. Accepting him as he is, is a good start. I suggest that pushing him a way happens because you're socially awkward. You don't know how to relate with him.
All of us feel and act awkward in some social situations. I suggest that once you are comfortable with yourself and him, you will feel less stress and less need to be upset at everyday situations.
I have a grandaughter who is 4 and one that's three. Both of them would have reacted in a similar way as your daughter. With the support of the adults in their life, they will begin interacting with the new people. For the 4yo,.it took several visits with her before she would come out of her room. The 2yo is less shy. She sat on her mom's for 15 or so minutes before going on with play.
After a couple of visits their aunt stumbled on a way to get them to accept her. She was putting on hand lotion when the 2yo wanted some. When her sister heard the laughter, she came out of her room. The 3 of them had a good time together. They've been good friends ever sense.
Perhaps you and your husband can find a way for your FIL to interact with the girls. Something simple and easy to do.
BTW when someone comes up behind me, for a brief second I'm startled. If that someone is a stranger, I'm uncomfortable and stay alert. When your daughter ran to you she was seeking reassurance that she's safe.
After your latest SWH I can better understand your reaction. I, too, was sheltered. My family was was conservative. I spent very little time away from them until I went to college. My parents taught me to be hypervigilant with people. I got the message that the world was a dangerous place. I was very shy.
Over the years, I learned that the world I lived in is safe. What a relief! Therapy got me started in thinking a different way. I'm 72 and a retired cop. I still believe my world is safe. I'm no longer shy. LOL