I understand that when your husband works away, you are essentially a single Mum of 3 children. And 2 of them you've not had much time to bond with. And this in itself is very challenging and must be difficult on yourself. It's lovely that you have a heart big enough to extend to other children who need it, not just your bio son.
May I ask how long you two have been together in total?
But I must point out that some of the language you use indicates your feelings towards this little girl in your care.
Firstly: "minipulates people around her so she is able to act like a baby with baby talk and crying etc, I used to comfort and love her now I just see an act and feel I need to get her out of this behaviour".
She is NOT manipulating you. She is a vulnerable little human, who's mother has abandoned her. You have stepped into that role, and amazingly she has reached out to even start calling you "Mum". With her mother abandoning her, her father absent most of the time, no friends at school and the only other guardian she encounters is a person who resents her. It must be scary, upsetting, un secure and lonely for this little girl.
Secondly: "Our sons even say they hate her ( I know this is normal sibling stuff) but she has no friends at school as she is horribly bossy and pushy and a know it all". - It is NOT normal for your biological son and her teenage (15) brother to say they hate her. This sounds like it's become acceptable to criticise and assassinate the character of this little girl in your house hold. I'm sorry to say, but this will have been initiated from you and it's your job to make sure none of the children are saying such hurtful and horrid, cold things about each other.
Thirdly " I just can't bond with her anymore when I have a beautiful son who misses out on so much because she is so naughty".
From this sentence, the resentment is clear. You resent her existence and you're upset that you have to spend any time on her that could be spent on your bio son. Which is heartbreaking to hear and I fear for the little girl.
It's in the little girls and the father's best interests if they involved family to help care for her or maybe a new step Mum who can extend her love as it will be extremely damaging for this little girl to live a lifestyle where nobody respects and cares for her. Every child deserves to feel loved, looked after and not made to feel a burden and rejected by their own parents.
You have this child full time, she calls you Mum, her bio Mum is no longer around. She is no longer a 'step child' she is your child. She is just as important as your bio child, if not more at this current time because of the awful issues she's facing in terms of being abandoned by her mother and brought up by another who resents her.
If you can not treat her equally then please for the sake of this little girl, move on and find a man who doesn't have children.
If you're so unhappy and crying all the time, this isn't good for your bio son either.