Aimismum your ex's g/f is jealous of a 6 year old, and the fact that she dont want your daughter at the meet up speaks volumes, she cant get away with lying whilst your daughter is there.
I think your daughter needs 1 on 1 with your ex without the g/f there, Im not saying withold contact, but I would reconsider the present arrangement with regards to your daughter staying over and being cared for by this girl.
Maybe a suggestion would be too limit the time spent over at the ex's house at any one time, but increase the days, maybe twice a week for a couple of hours, rather than once a week overnight (if that is the arrangement). I personally would push that when your ex has your daughter that he takes her out for a treat and spends quality time together, just the both of them without the g/f being there, its not the g'f job to look after your daughter and I doubt very much that you would want her too either.
You are a lot calmer than what I would be if that was my daughter, what this girl is doing is classed as child abuse, and it was me I would have been straight round that house having a word in her ear out of earshot of her mates and your ex I understand why you are trying to be calm at the moment and wish you luck for the meet up if it comes off xx