I would probably try to explain to her that there are all sorts of different kinds of love. One kind of love is 'mommy-love', this is the love a mommy has for her child/ren where you want to see the person you love grow/prosper, keep them safe, be happy, etc... there is also 'child-love', which is the love a child has for their parent, this love means you look to them for guidance, care, acceptance, comfort, etc... 'brotherly-love' the love of siblings (biological or otherwise) have for one another-protection, safety, testing boundaries...and then there is 'adult-love' which is the love two adults have for one another where they want to be together because they make each other so happy, feel good, blah, blah, blah. Different kinds of love call for different types of behaviors to express said love.
Use your own definitions of/for the different types of love. Same sex relationships can be confusing for kids, and I think more so when the child is the same gender as the parents. My sons seem have a harder time with their fathers relationship than my daughter does. Does your daughter have exposure to other same sex parent families? I think that could really help as well.
Sorry if I am not much help, I am kind of just winging it, too :)