To build on a lot of the advice here:
Your mother clearly has issues.
For some bizarre reason, she needs her children to be perfect, invincible, invulnerable - 'successes' - in order for her own sense of self and safety not to feel under attack.
She can't cope when things 'go wrong' in the life of one of her children, for example, with your divorce. Instead of seeing you as someone who left a bad relationship, and who builds a new life after that - as someone 'strong' and 'capable' - she's freaked out by the evidence that life can throw up obstacles, and careful structures can fall apart.
I'm guessing she's really strange when you need to ask her for any kind of help - be that really small emotional claims on her, or even when asking for love and caring.
Some people are like that. I think it's because they are put together in a very fragile, brittle way, and this is how they cope.
The result is that they tend to put people in 'boxes' ("That's my 'difficult' daughter; that's my 'good' child."), partly because it cuts down on the need to think or engage. Partly because it reduces the emotional demand - which they find overwhelming.
One way to deal with her would be to acknowledge that she is deeply flawed and in her own way, struggling to manage with the demands of life and relationships with the people in it.
Another way is to acknowledge that your relationship with her is stressful and produces anxiety. Then to acknowledge that this is not a failing on your part. You will have been subtly told that it is your fault for many years. It isn't. She has issues. It IS going to provoke anxiety when you interact with her because she is acting in very non-rational ways and you are having to do all sorts of mental gymnastics to keep the relationship with her. You are carrying the stress for her. So of course it makes you anxious.
Once you acknowledge the reality of this, you can begin to make clear-sighted decisions with regard to your relationship. For example: "Interacting with my mother is anxiety-inducing. This is bad for me. I can't change her. What can I do to lessen this very real impact on me?"
And the solutions to that may well be to reduce interaction. It may also be that knowing all of the above means you can detach quite a lot. Realising it's her issues goes a long way. But you really have to work on that insight.
And of course she's good with the children. Children are very trusting and non-judgmental. they are a great ego-boost for the fragile. The wonder, of course, is that - even with children being so trusting and accepting and giving of unconditional love - she couldn't cope with you (or even your sibling) when you were this age.
So, in a way, not only is she getting all that non-conditional love from the children, she is also getting some sort of fantasy validation that she was great when you were young - she gets to re-play it AND it 'proves' to her (And ,she hopes, you) that the problem in your childhood was you, not her.
It's bollocks though. for a start, you're their mother, she's only there sometimes, and you're facilitating their interactions with her now.
And she knows that.
As they grow up, it will almost certainly unravel a bit. 
But you will probably be able to have adult conversations with your children about the good and bad qualities of their gran.
Does any of this help? I do think that the place to start is to realise that your mother is a person who has issues of her own and that it is absolutely not your fault that the relationship makes you anxious. There are good reasons for that sense of anxiety and you are allowed to take actions that reduce that stress. Start listening to yourself, start taking yourself seriously, start putting yourself first a bit. Try imagining one of your children telling you what you are telling yourself - and thinking about what your answer to your child would be. It's good for you. 