E.S.
I can understand your concern for your daughter's well-being while in the care of others, even if it is your mom. Sometimes new mom's have some competition with their own mothers, not that I'm saying you do, but I did with my mother. So, every now and then I'd be more critical of her than others.
Anyway, kids need to experience everything that is safe for them to experience. This includes exploring, adventuring... and yes, hurting themselves. How will your daughter learn not to run on the driveway if you do not let her run on it and slide in the sand? How will she learn that climbing over rocks is dangerous?
Little ones learn by experiencing, it's in our nature as humans. As long as it's not overly dangerous and someone is there to keep an eye on her, I think you are fine to let her get these scrapes and bumps.
And, your mother may be lest restrictive to her activities. I remember that I kept an extremely tight fist around the food and drinks my daughter got when she was a toddler. I was so anal about it. I thought any infraction might cause problems for her... then one day my mom and dad took her to the mall. I told them, don't give her anything bad to eat!
They brought her back to me with a huge blue face. She had a raspberry misty with grandpa and absolutely LOVED it. And she was soooo cute... I had to take a reflection and say, "why am I so worried about it?"
My mom is very wise... she has been through it all and seen it all. She raised me and my brother and her mothering style seems different to me sometimes... but I'm seeing her in grandma mode, with over 30 years of mothering experience.
Now... there is no better person to care for my children than my own mother.
I don't know if this helps you in any way, but good luck.