My 2 year old and my fiances 3 year old wont stop fighting... Can i make it stop?

My fiance and I each have a child from a previous relationship. His daughter is 3 and my daughter is 2. His daughter wants to be the center of attention, while my child is okay with playing on her own. However, my daughter does NOT want his daughter to have my attention. His daughter has started lying and throwing fits, saying "I'm going to tell my mommy" when she doesn't get her way. She throws herself on the ground and says my daughter pushed her when my child is 5 feet from her. I am at my whits end. I love his daughter but I hate that my daughter is getting the crap end of the deal. I know my daughter is not angel, she is 2, she gets fed up with having everything snatched from her by my fiances daughter, and she hits. But how do I get her to stop when his daughter is in the wrong too? We were so hopeful that with them being so close in age they would be great friends but instead they cannot stand each other... And they are not this way with other children! They act great with other kids their age!! The worst part is, we only get his daughter every other weekend and on school breaks, so every bit of progress we make (which usually isn't much) gets erased in the 11 days her mother has her... What do I do now???