Mixed family issues.

Hello, I have posted on here before and gotten some great feedback and i hope to have the same constructive feedback this time as well. I am a 29 year old man, I have been with my fiancee for well over 3 years now, I have been a step dad to her 2 girls (9 and 7) for the duration as well. My fiancee and i just had a child of our own and i am having some major issues popping up out of the step girls now that the new baby is here. Yesterday i was informed that my fiancee had shipped off the girls for well over a week and plans on taking my son and leaving me alone on the 4th of july, the reason being that there is a story that the girls are telling of me grabbing one of them by the throat, slamming them up against a wall and yelling at them. Something i might add NEVER happened. Not only has my fiancee been home for the last 4 months straight there have been absolutely no issues even remotely close to this that have happened. I am not abusive, i do not get physically violent with them and the worst thing they get out of me is telling them to do chores. This isn't the first time they have outright lied about me and said something to the extent of me being abusive to them, however my fiancee is acting like she doesn't believe me at all and to a certain extent i understand that it's hard to not believe your own kid when they are conveying a story like this. My issue is this: I have bent over backwards to be a good father figure to these kids, i have put a roof over their heads, food in their stomachs, clothes on their backs, rooms full of toys and more. As a new parent and as a new step parent i have absolutely had moments of being a little too hard on them or reprimanding them very bluntly or snapping at them but i have never been abusive. I fear that all of this new stuff is stemming from the "competition for attention" that comes with a new baby, with a new father that is not their own. They started this lie with my fiancee's mother whom came into town to visit and has been giving them ample amounts of attention where we (my fiancee and myself) are probably not giving them the attention they crave. They started by telling her this story, then they decided to tell this story to their biological father and his parents. They say they are afraid of me even though i have done nothing to these girls to strike that kind of f ear into them, they say they want to move away from their mother and myself because of this, asking at what age can they move out. This obviously put her in a very bad spot and me in an even worse one because i know if she decides to leave she is going to try and take my son from me. And worse i worry about even more of this same stuff happening in the future and just getting more overblown. I understand the emotional mess that kids can be when they have to be split between two parents but i honestly feel like I'm being sabotaged and both my son and myself are going to pay a high price for their lies and manipulation. I have heard horror stories of step kids painting their step parent out as some sort of monster because deep down they are bitter and angry and i worry about the future. Any step parents out there gone through something like this? Any advice? I am heartbroken that these things would even be said about me considering all i do for them but i am even more worried about losing my son because of it. I have nothing to hide and i stand firm on the truth but my life has been thrown up in the air because of 2 step girls who are trying really hard to lie about me and something that never even happened. Please help, any thoughts would be welcomed. Thank you.

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