Dude - I am fortunately (or unfortunately, depending on how you look at it!) well versed in the ways of the Mother Xs of the world and was on to her potential to negatively impact on dd's and my relationships within the school from day one. She has indeed already enlisted a number of the strategies you mentioned (criticizing me to others, suddenly establishing friendships with the parents of kids dd is playing with - people that she 'despised' a day earlier, and so on). I have some tried and tested strategies to deal with such situations (which basically consist of not taking anything she says or does personally, cultivating friendships and, while indicating my disagreement on various issues, being unfaltering in my civility which gives her very little to use) - all of which you no doubt employed too - and while they don't guarantee that I'll avoid all out warfare, they have stood me in good stead so far! But you are spot on; she has the potential to make an unpleasant experience into an horrendous one. Re badgering the parents enough, this little girl has said to dd 'just have a tantrum if you don't get what you want - that's what I do, works every time' and Mother X has told me the same thing! Dd knows me well enough by now not to bother - tantrums don't fly with me, so she hasn't tried this particular tactic
Our efforts with our Girl X weren't really effective, because while she did learn that certain behaviors wouldn't work with us, she decided to focus on manipulating DD into going over to her own house, where our rules did not apply and Girl X had all the power. Once there, GX limited them to only two activities, didn't let DD play with any of her toys, and Mom X involved herself in every argument, where apparently she sided with GX every time. Needless to say, DD didn't like going there.
So that's something to watch out for.
