awww you poor thing.

Personally I think it is ok and actually healthy to apologise to our kids when we make mistakes. As a parent I ask ds to apologise when he has done something wrong to me and I think it is only fair that I too apologise if I do something to him that wasn't right. So if you arestill feeling bad thats probably what I would suggest. I would reiterate that her behaviour was still unacceptable yada yada yada but that you shouldn't have had that reaction and of course you don't want her to run away you just want her to behave yada yada yada that way it is cleared up and Lily will know that of course you don't want her to run away (which I am sure she already does) and u don't have to feel bad anymore