I think @jamiefraserskilt has it spot on.
OP, you can't change what happened in your childhood and you probably can't change your parents' reaction to it now, either. You're never likely to get what you want from them. What's important now is what you have mentioned, the future of your child.
This was something that worried me too as my parents were pretty shit, to be honest. I knew I wanted to do things differently but wasn't sure I'd be able to. Luckily enough, I took what I'd learned NOT to do from them and I think it's really helping. I know my relationship with my child is completely different to mine with my parents and I really feel we've dodged a bullet.
Furthermore, I was also worried about their grandparenting but, as so many people say, they are completely different with my daughter and are in fact excellent grandparents. They would never admit to any parenting failings of their own but I'm pretty sure that they prefer the way I do things with my daughter.
My mother was also one of those who wouldn't give you a day off unless you were really dying. The result was that I was quite badly injured in my early thirties, but the whole 'mustn't make a fuss about nothing' attitude was so deeply ingrained that I didn't seek medical help. I didn't realise the extent of the injury, nor did my parents, until I did have to seek medical help. When they found out how serious it was, my mother couldn't understand why I hadn't seen a doctor earlier and I had to explain that it was her treatment of us when young that had left me feeling I couldn't see a doctor unless it appeared to be actual life or death.
She laughed and dismissed that idea but I could see it affected her and ever since she suggests I see a doctor for a broken fingernail! If I ever even wince she takes any suggestion that I'm in pain very seriously, so I can see the incident affected her - this and a couple of similar issues.
She learned her lesson - way too late and will never admit it, but I know that she knows she was wrong. Your mother is probably similar but I don't think you'll be able to do anything about it and it doesn't mean she wouldn't care for your child properly. All you can do is monitor their relationship and act accordingly, rather than based upon your own experiences with her.