what are our chances of winning an appeal?
Impossible to say, I'm afraid, because it depends not only on your case, but on how strong a case the school will put forward for resisting further admissions. Have you read the Q&As, section C?
Will the fact that my second daughter has a place at a school we placed as her first choice be an obstacle?
Not necessarily, especially if you have good reasons for changing your mind.
A panel is likely to inquire whether your daughter is happy at the grammar school, whether she has friends there, what exactly the comprehensive school can offer that the current school doesn't, whether 1-2 months is too soon to take such a decision, etc.