Try to communicate openly, honestly and without anger. Good luck to you. My girlfriend and I are moving in together soon. Some things will have to evolve as the relationship evolves. It is important to discuss this because you and your girlfriend will have various responsibilities.
Manipulation becomes more difficult if there is a solid framework of rules and expectations.
Many young girls will feel threatened when there is a new woman in their father's life. They will feel that their own relationship will be pushed aside. You need to reassure your daughter that her relationship with you remains strong. Spend some time with her by yourself. Let her know she can always come talk to you and that your new girlfriend cares for her a lot and thinks highly of her.