As an outsider entering a house as a child carer, I have some advantages when working with the children that the parents don't have. This is entirely because I am a new entrant into their lives and they don't yet know what I will do and how I will react to different behaviours. They will not waste time in finding out my reactions, the honeymoon period seems to last about 3 days before some serious testing begins. The advantage though that I have over the parents is that the children and I have no history together, the child throws a tantrum more as an experiment and, when it doesn't work, moves on to other strategies. Because a parent has history with the child, the child recalls that once, when I did this, I got what I wanted. This means that if a parent wants to break behaviour patterns between them and their children, they need to work much harder and longer then I do when I am simply setting them up. If whining, or tantrums, or nagging or persistence has worked in the past, the child will take time to realize this is not the case now, and the parent will take time to break their own part in the pattern. Also the children won't want to change a system that is working great for them.
Some things I have noticed;
Winning battles against children is like quitting smoking, every battle won is hard and it brings you one step closer to easier times.
Every battle lost means you need to win 10 to convince the child that this won't actually be a common pattern.
I find it helpful to look at them as battles, the children change tactics like lightning and we need to be ready to counteract them.
Children will always push boundaries just to see if they are still there, holding firm will actually reassure them, they may end up on the floor and screaming, but they will actually like that you are not such a pushover.
Remember as well that children are allowed to "lose it", I lose it sometimes, so can they. Telling them to stop, following them and trying to make it better or yelling at them won't help, just letting them get on with it and cuddling them afterwards is the best way.
One last thing is if you find battles always happen when you need to be somewhere else then feel free to set them up when you have time to follow it through. It is remarkably easy, just ask the child to do something you know she won't want to do. Have strategies in place to deal with the tantrum that will arise, then when she has done the whatever it was, give her a cuddle and say thank-you.