Salaam fruitcake.
Unfortunately there are many men who will ignore what islam really says about a husband's/father's role and focus on what the wife/mother should be doing 
In a nutshell, once the mother re-marries, then the father should take custody of the child. There are various schools of thought who differ slightly, but the consensus is that a mother's re-marriage puts the child in father's custody - unless the mother is married to someone mahram to the child. In this case, mother still has the bigger right to custody - should she want it.
With regards to your husband, it was short-sighted of him to not discuss the possibility of his daughter living with you. As an outsider to the situation, it seems obvious that a father who wants to have a relationship with his daughter, will want to have his daughter live with him, should the opportunity arise.
With regards to your house, make sure you protect it and your children get a fair share from it.
Your question about refusing to look after a step-child. It is a father's islamic duty to provide. Your ex-husband has done a great injustice to your children by not providing nor contacting his children. Similarly, your DH would have been guilty of a great injustice had he not provided for his daughter nor taken her into his home. Islamically, he could not leave the daughter with the mother, when both mother and daughter want father to take on that responsibility. With in-laws, it is clear cut, wife has no obligation to be serving them. With a child, it is harder to say that a step mother can refuse to play a role of a carer in the step-child's life, especially at age 12. The father is still the main person responsible, but once re-married his wife does become a step-mother and islamically that role demands that she is kind to her step-children and that the children are kind and respectful back. I dont know how a family unit would exist without both husband and wife making an effort to bond/spend time with their respective step-children. I would guess that a mutual effort would have to be made where both husband and wife feel that they are giving and taking in equal measure. Unfortunately, in your case,it seems that you hVe done all the giving.
You are islamically under no obligation to look after your husband's parents. Your step-daughter is married now, you dont need to be freeing up your weekends to entertain her and her husband, you husband should be able to manage that. Do continue maintaining good family ties with her, but also put your own children at the forefront too. You will have to be a bit more selfish now and be there for your own children.
A detailed answer to your question about father not providing for his children: c&p'd from islamqa.com:
Maintenance of children is obligatory upon the father according to scholarly consensus, whether the wife is poor or rich. So she is not obliged to spend on the children if the father is around.
If the children are in the custody of a divorced woman, then their father must support them, and the mother who has custody of a child who is still breastfeeding has the right to ask for payment for nursing the child.
Maintenance of children includes accommodation, food, drink, clothing and education, and everything that the child needs, and is to be based on what is reasonable, paying attention to the husband’s situation, because Allaah says (interpretation of the meaning):
“Let the rich man spend according to his means; and the man whose resources are restricted, let him spend according to what Allaah has given him. Allaah puts no burden on any person beyond what He has given him. Allaah will grant after hardship, ease”
[al-Talaaq 65:7]
This varies from one country to another and from one person to another.
If the husband is rich then he must spend according to his wealth, and if he is poor or of moderate means, then he must also spend according to his means. If the parents agree upon a specific amount on money, whether it is great or small, then that is up to them. But in the case of dispute, the one who should decide about that is the qaadi (judge).
With regard to custody – as defined by a number of scholars – it means taking care of the one who has not reached the age of discernment and cannot live independently, and raising him in accordance with his best interests and protecting him from anything that may harm him. Rawdat al-Taalibeen (9/98). What is meant is taking care of the small child and looking after him. So the main issue of custody is taking care of the interests of the child. Hence if the father refuses to undertake this duty towards the child, which includes maintenance, then he is sinning, and forfeits his right to custody. It says in al-Rawdah al-Murbi’: The child should not stay with one who does not protect him and take care of him, because that is contrary to the purpose of custody. Al-Rawd al-Murbi’ (3/251).
Ibn Qudaamah al-Maqdisi said: Custody is aimed at looking after the child, so it should not be given in a way that will be detrimental to his welfare and his religious commitment. Al-Mughni (8/190).
Ibn al-Qayyim said: If we show precedence to one of the parents, we must pay attention to how he looks after the child. Hence Maalik and al-Layth said: If the mother is not in a safe place or she is not of good character, then the father has the right to take the child from her. Similarly in the well known report from him, Imam Ahmad said that it depends on his ability to take care of the child. If he is careless or unable to do that, or is not of good character, or he is immorall and the mother is different from him, then she undoubtedly has more right to take the daughter. Our Shaykh said: If one of the parents fails to educate the boy and raise him in accordance with Islamic teachings, then he is sinning and has no guardianship (wilaayah) over him. Anyone who does not do his duties as a guardian has no guardianship. He should either be dismissed as the guardian and replaced by someone who will do what is required, or someone else should be appointed with him who will do what is required along with him, because the aim is to obey Allaah and His Messenger according to one’s ability. … If the father marries a woman who does not take care of his daughter, and her mother is better able to take care of her than this co-wife, then custody should definitely be given to the mother. Zaad al-Ma’aad (5/424).
Shaykh ‘Abd al-Rahmaan al-Sa’di said: But if one of them neglects their duties with regard to custody and care of the child, then he forfeits his guardianship and the other should be appointed instead. Al-Fataawa al-Sa’diyyah (p. 535).
Based on this, if the father refuses to spend on his children’s maintenance, he forfeits the right to custody, even if his refusal is aimed at hurting the mother. This indicates that he is not to be trusted to take care of his children’s interests. The mother has the right to ask him in court for maintenance of his children.
I need to charge my tablet. Will answer your other questions once charged inshallah.