Moomintwo, I'm so deeply sorry about the loss of your dd. It must have been a very traumatic time for you and your family. And to have your husband run out on you afterwards - wow! Clearly, you've done a great job raising the remaining kids on your own, based on what you've told us.
I'm sorry, too, that you're disappointed in your gp experience so far. Like others, though, I think this is more about dd's concerns about her child than it is about her view of you. I don't think it's that she doesn't trust you , just that she's not ready to let her child out of her sight. Whether it's because of the loss of her sister or she's just a very protective mum, idk. But, imo, it doesn't really matter. Please try to respect how she feels and stop trying to get to spend time with gs alone. If she sees you respect her feelings,, she may loosen up in time.
But even if not, at least, you can have a lot of fun times together, the three of you (or 4 if you can include the dad sometimes). Then you can focus on the good times you do have instead of on what you're not getting. And you will still probably have gs alone "by default," now and then, so there's that. Again, I don't think it's due to lack of trust that she doesn't leave him with you otherwise, so please just treasure those special moments and don't look for deeper meanings (I know it's hard not to).