Why does my teenage daughter treat me so horribly?

She is a lovely girl and can be very nice when she wants to.She is polite and very well behaved at school,is intelligent and charming.However,she knows exactly what annoys me and some times goes out of her way to wind me up.I really do try not to rise to the bait but find it extremely difficult.she is 16 and has been like this since first year.My other daughter is fifteen and although she gives the normal teenage cheek,She never upsets me the way "Janet" does.It is as if she thinks her family is not as good as her and she constantly puts doubts on my intelligence .She also cannot stand being in the same room as my eldest son but trys to baby my 8 year old daughter.We are going on a family holiday soon and I want everyone to have a good time and for us to all get on together.I try to give all my kids equal attention but even if I take my daughter out seperately we always end up argueing.I just want to get on with her as well as i do the rest of my family.I got on well,and still do with my mum.What am I doing wrong? please help as I love her dearly but it is not fun walking on eggshells all the time.