I was thinking about your situation today, as well as my BFF's relationship. She's been in a loving relationship (but separate households) with a man for the last 12 years or so. At first she was a mistress to a married man (although his marriage was well and truly over, he and his wife just lived under the same roof for convenience sake). Then a couple of years later, his wife died, leaving him with a difficult child in his late teens who hated his father (due to the very dysfunctional relationship with the mother, who put all her emotional eggs into the basket of her son and not the marriage). So of course he kept his own counsel with my BFF to protect his son. And my BFF from the son's wrath.
After another two years he finally told his son about my BFF. Son was initially hostile, even though he was now an adult with his own career. Dad really puts a lot of time into his son, perhaps over-protects him.
Now - my BFF spends a lot of time over at his house, son now accepts her and they get on well. But my BFF and her boyfriend still keep separate households and still do not look like moving in together. No plans yet to get married. They've been on holidays together, friends and family on both sides recognise them as a married couple (he "gave away" her daughter when the girl married), but his son is still not ready for his dad to remarry, and so they continue to maintain their relationship physically apart.
It works for them. The young man has needed his dad to take his time, because his mother did a lot of damage by making him the centre of her world, and now she's gone and he is still struggling emotionally to grow as a person.
This is what some people do, in what can be extreme circumstances.
There are other sole parents (male and female) whose primary goal, it seems, is to find a "replacement parent" for their children. They may not even realise that is what they are doing, but it is a recipe for disaster. "I love this person, my kids enjoy seeing him/her when we go out on picnics together, we'll be one big happy family," only there is a lot more to it.
Another good friend of mine had tried to hold her marriage together when her husband's schizophrenia became so out of control that he was spending most of his time in a psychotic state and believing he had to save the world by killing his wife. There's only so long you can hold a marriage together, under those circumstances.
Another bloke came along and they had so much in common it was almost magic. He loved the kids but did not interfere with her raising of them. She married him a couple of years after they met, when her daughter was 6 years old. They were once again a two parent family. He would mind the kids while she worked and studied, he encouraged her to undertake more study and changed his work to home-based, so he could be there for the kids. it all seemed wonderful - then when she was 16, daughter told her mother her stepfather had been having sex with her from the beginning. Stepdad had in fact married the daughter, not the mother (in his mind). He was, it turned out, a pedophile of the highest calibre, in terms of his skill at recruiting. He had my friend convinced it was all her fault, and that she had to save the marriage. There was a lot of other sordid stuff in there and as my friend began to unravel it all, she was finally able to begin to see clearly and to boot him out. Again - a marriage that couldn't be saved, because in this case the marriage had never truly existed. Not with her.
My point - people marry for all sorts of reasons and in all sorts of circumstances. There is often a lot of history in a family, before the step-parent joins it. It takes time for this disparate history to mesh with any success, and as it begins to mesh, those gears often grind. If you don't ease the clutch as you go, those gears will grind off teeth and the machinery of the marriage can get damaged or even broken irreparably.
It is not uncommon for marriages to begin too hastily or for the wrong reasons. That doesn't mean it is doomed to failure; but it generally means that a lot more hard work has to go in, from both sides, to save it.
Anyone who has married expecting an instant partner and co-parent, needs to recognise that with their own kids, the bio-parent must always take precedence in their handling. There still needs to be delicate balance of involvement of the step-parent, as well as teamwork. But the buck has to stop with the bio-parent. They have to support their family, have to actively work with their children but also balance it with their newer responsibilities with their new spouse.
It takes effort, brains, commitment and honesty. Honesty with self and with partner.
I would suggest family counselling, especially with a view to setting up strategies to help you both work as the right sort of team, in every aspect. As well as strategies for both of you, each in your own responsibilities, to know how to handle this girl. At the moment she's being a brat and is getting away with it. She's probably also desperately looking for a father to properly parent her, to show her what is acceptable behaviour and what is not. If he doesn't do this, he is setting her up for failure in her relationships as an adult.
Her welfare needs him to be a good, effective parent.
As for the younger one - he should, by rights, be making sure she also gets her share of his attention. But something YOU can do while he leaves her with you - make sure you can imprint yourself on her as a good person who cares about her and who she respects. You have a chance her to make sure little sister won't necessarily follow in big sister's footsteps, at least not with you.
Of course you shouldn't have to do this. But you have that chance, and it could be very useful for you.
Marg