Sounds like you know the triggers and I would be inclined to seperate them before it escalates to the point that your DD is biting; that way she knows that the other child's behaviour isn't approriate either. At this age they are just reacting and we need to teach them to share and to be gentle etc... If the other mother isn't willing to step in then I would just gently try and distract your DD with another activity or the other child.

Children bite, lucky for me DS mainly bit me and eventually the phase passed