Advice needed - family relationships

When I was a kid, my mom was paranoid about my sister, my brother, and myself. She was worried about everything. She considered her primary goal as our mother to keep us safe, at any cost. We could never do a lot of things other kids did. For example, we lived in an extremely safe residential area, about 5 blocks from our elementary school, but were not allowed to bike to school until several years after our peers. We could not go away to summer camps. When my twin sister and I both got accepted to the university we went to, my mother deemed it too dangerous and insisted that if one of us go, the other had to go too, and we had to room together.

One of her primary ways of keeping us safe from strangers when we were young was to constantly tell us all the terrible news stories about bad things that had happened to other kids. (I'm assuming in retrospect that they are true, but for all I know, she made them up). Stories of kids who were abducted, tortured, killed in various ways. Kids who went into public bathrooms alone, who allowed strangers to speak to them, kids who were "too friendly". I remember feeling panicked as a child after she would tell me these stories. I think they helped me grow into an adult who is anxious, uncomfortable around people I don't know, and really socially awkward. I'm sure part of it is just who I am, but I can't help but feel that this contributed. Certainly it gave me a lot of fears and nightmares as a child. (Ironically, my mom never understood why I had so many nightmares).

Turtle is a very cautious little boy, but Tadpole is bright, cheery, friendly, and outgoing. At the Christmas party we had last week, I saw her in many different people's laps. She likes other kids and people with dogs at the park. She says hi to everyone whenever we go out anywhere.

My mother has commented on her friendliness several times, and has said "we'll need to do something about that", or something to that effect. The first time it happened, I was alarmed but didn't say or do anything, just filed it away in memory. Now I'm getting concerned, and I'm not sure how to handle it.

Luckily, in some ways, my mother can't handle watching the kids alone, so I'm never in a position to have to refuse to allow her to babysit or spend time with them, since I always have to be there anyway. Also luckily, she doesn't see them THAT often - twice a week at most, and usually only once a week. But on the other side, there are plenty of other things she says and does that I'd like to shield my kids from - her snobbish attitude, her racism, her elitism. As a parent, she was overanxious, overprotective, overbearing, controlling, and manipulative. I don't want her to be close enough to them to pass any of her issues onto them. On the other hand, she is their grandmother and I don't believe in completely cutting off their relationship - she has her good attributes, and I don't want to shield my kids from all the negative things in their life, either.

Now that I'm writing this, I am thinking I shouldn't say anything, just be always present and always careful of what she's saying and how she's saying it. But ... I am uncomfortable and unhappy to have to be on alert at all times.

What would you do in this situation?