Surely she has no real right of access anyway, as she isn't the parent?! - she may have no criminal record but that's not the point!
Your solicitor seems to be saying that she wouldn't get very far anyway by telling you to just continue refusing access - can you get more advice on this? As in, you may be shooting yourself in the foot going down the supervised contact only route when it could come to court only for the judge to agree that she has no right at all.
If it were me I would indeed continue to refuse access completely. She is not the parent. You also consider her a danger to your child by virtue of the fact that she is sympathetic to your ex despite his behaviour towards you and his threats against the child. She has witnessed his appalling behaviour yet has him now living with her. So supervised contact may not be appropriate as there would be presumably no possibility of it moving to unsupervised - it would not be the start of a normal grandparent relationship.
You could say that you consider her action in bringing this to court an aggressive move which is merely designed to intimidate and upset you and say that it is orchestrated by her son.
Make sure all those threats, especially those to kill and to abduct your daughter, are presented to the court, and say that in your opinion she is as much a danger to your child as he is - she is NOT neutral, she has him living with her and is sympathetic to his hideous behaviour.
But most of all take advice - can you get some free time with another solicitor? - on whether this attempt is actually just likely to be thrown straight out. Also, if you end up representing yourself, maybe Women's Aid, for help on how to present your argument?
Failing all that, I would be looking into moving away!