Stepchildren?! Advice please!

I have three stepchildren 15,12,10! Their father and I have been together for a year and a half, have been married for a year and four months (Yes we married quickly but we have known eachother since 2012) and we have a five month old daughter. Even after all of this time and their sister being born they still don't accept me in their life as a parental figure, it's a real struggle because their mother despises and talks badly about me to them. My stepdaughter has even gone as far as to try to shake up our marriage with lies to her father and to her biological mother. Does anyone else have this problem? Why won't they just accept their father and I are very happy and I'm not going anywhere? How can I get through to them?