He married her without the knowledge of his first wife, then his secret was found out, and he is still not giving her her rights with regard to his staying overnight with her

I got married four years ago to a man who was already married and had a daughter. He told me that it would remain a secret to his wife and father, until they found out from people and not from him, and I agreed to that. From the day we married, he has not slept at my house except for one week, on the basis that he was travelling. After that he has not slept in my house and I have been living on my own, and he comes every day. I got pregnant from him and gave birth to a daughter, who is now two years old. Until today he has not registered her in his name, for fear that his wife will find out. I have been patient all this time and have said it doesn't matter, because frankly my husband is a man like no other and he loves me, but after 3 1/2 years his wife and his father found out, and she asked him to divorce me, but he refused to divorce me or to divorce her. But until now he is not treating us fairly, and he has never stayed the night with me and my daughter, and he has not registered his daughter in his name, and I do not know why. Even on Fridays it was hard for him to come and visit us; even when my daughter was sick at night, I could not tell him and I was always the one who took her to the hospital. I do not know what I should do. By Allaah, I always ask Allaah to give me patience because I have suffered all these years and I do not know for how long. Please note that my husband fears Allaah and does not miss a prayer, and he always does good. Every time I argue with him he tells me: “Everything in its own good time; you have been very patient, can't you be patient for longer?” 
I hope that you can help me because in fact I am not able to put up with this injustice any more.

Praise be to Allaah.

Firstly: 

When a husband conceals his second marriage, in most cases that leads to some kind of injustice for his new wife, as he will be confused and uncertain and will be afraid that he may do something that would lead to his first wife finding out that he has taken a second wife. This may lead him into a series of mistakes. 

As you agreed to that at first, then you have to put up with what happens to you in some ways and you have to try to set things straight in other ways. 

If your husband had an excuse -- in your view -- before his marriage to you was discovered, then he has no excuse now. What he has to do is to teach you and his first wife fairly with regard to spending the night. However many nights he spends there, he has to spend the same number of nights with you, and you have the right to demand this right which Allaah has obliged him to give and that Allaah has given to you. If he persists in refusing, then you have the choice: either you can accept your life with him and put up with it until Allaah grants you relief -- which is what we recommend -- or you can choose to leave him. 

As the matter has been discovered, we advise you to appoint as an intermediary someone who has knowledge and is of good character, who can intervene between you to resolve your problem with him and make him do that which Allaah has obliged him to do of treating you and his first wife fairly, and registering your daughter officially. This is something that is essential. How can he accept for his daughter to remain like that, with no recorded lineage and with her rights exposed to loss? 

Now the matter is up to you. Advise him and remind him of Allaah, and if he does not respond, then appoint as intermediaries wise people from among your family, or from among your family and his, to advise him and make him adhere to that which Allaah has enjoined upon him of treating his wives fairly and registering his daughter in the official records. 

Ask Allaah to help and guide you and him. We ask Allaah to bring you together on the basis of good and to make it easy for you to do that which pleases Him. 

And Allaah knows best.