A.,
From someone who has married into a divorced family and I also come from a divorced family, we have 8 parents to contend with since they are all remarried. You are the parent and you are the one that determines the rules and schedules of your daughter.
Please stand up and let your parents know, if they are going to behave in an immature way you are going to have to take care of your daughters best interest first. You need to let them know they do not need to "try" and communicate with each other when it comes to you daughter. If they are in fact divorced (separated) and when your daughter comes to stay with them individually they are going to have to respect and not question your parenting or each other. It would be like my husbands parents telling my parents what they should and shouldn't be able to do. When our son is with one set the other three just deal with it. They don't call each other and get into each others business.
Flat out, you can tell your parents; either they start respecting your parenting and stop dragging your daughter into the middle of their own agendas and opinions or they can just be taken out of the equation until they can handle themselves in a way that is best for your daughter. Tell them they had their opportunity to raise you and now it's your turn to raise your daughter, not them. Tell them if they break the rules just once, that's it and I would follow through just to teach them a lesson.