[bevy]

I am raising my 4 year old cousin right now. We had so many of the same questions. We have just let things happen as they do...she now calls dh daddy, after a year and a half of being with us. We refer to each other as mom and dad, as we do with the other kids. That way, it is not different for her than the other kids and when she was ready she made the switch. She calls me mom part of the time.
I refer to her biomom as her birthmom now as she doesnt really ever see her and thats what she hears us call the other kids (both adopted) bioparents.
Make sure to get something legal where you have full guardianship. That way, you make all the legal decisions for this little girl and your sister cant just come in a nd take her if she feels like it one day.
HOw old is Lucy? Does she know at all what is going on? If she does, then I would keep everything open until she is ready to transition emotionally.
Good luck