Sounds like you would benefit from looking at narcissistic abuse. There's loads on YouTube that you can watch while driving, washing up, doing any mindless task that stops you actually reading a book to inform yourself.
If you think of it as that he needs every person, every situation, every moment in life on this planet to evolve around making him look good, then it will answer your question. He will reframe the situation with your dad to make him look good. He will distort every reality and twist every meaning, but you cannot waste your life running around after him, trying to set the record straight. Not with yourself, not with your friends, not with his new girlfriend, and certainly not with your child.
A previous poster suggested you are sometimes vague in your reply, such as saying that there are two sides to a story, and that is not quite how you recall it. A good question to ask yourself would be: how will knowing that the relationship with her grandfather was not as wonderful as he's making out, help her in any way? The chances are, it won't help her at all, and even though it's not the truth, being told that would undermine her fathers perspective and how would actually help? Would it help her realise he's a liar? Well there are other ways to do that. He will teach he that himself. Would it help her to think of her dad, making her mum more miserable when she lost her father? Not really. If she needs to know that he's unsupportive she's going to find that out because he is going to demonstrate that to her in due course.
It's terribly hurtful for you and out of your protection towards your daughter, if you want to warn her what he's like to spare her. But, she's not the new girlfriend; she's the daughter and that is a different set of rules. That's not to say, you need to lie, And certainly never cover for him, but it's your daughter you are protecting by not taking her through every situation, pointing out the reality of how it really was. Is it going to harm her to think her Dad was nice to her grandad? No. Is it going to harm her to think her Dad is lying and was horrible to her grandad? I suspect it probably is because even if he was horrible to Grandad, it doesn't necessarily mean he's going to be the same to her. What I'm saying is, some battles should be picked wisely. It's different. If he is telling her, 'Mum says I was horrible to Grandad, but I was really nice to him'. That's a lie, and that is essentially undermining you by saying you are not telling the truth, and this would be a good one to lightly say, 'It's a good thing there are two sides to a story, because that is totally different to my version'. It's okay, just say to her that one day, when she's older, you can talk to her about these things, but now she's a child and doesn't need to be bothered with adult stuff.