All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We ask Allaah to reward you with the best reward for your keenness to ask the people of knowledge, to know the rulings of Islam.
We advise you do not bother much about the marriage of your husband since he might be truthful in his claim that he did not marry another woman. If he did in fact marry another woman, then you should remind yourself that Allaah is The One Who made this lawful for him. A man is not Islamically obliged to inform his wife about his second marriage. Probably, he did not inform you not to hurt your feelings.
However, it is obligatory on your husband to be just between his wives if he has married a second wife; it is obligatory on him to bear both your expenses and provide you with clothing, and accommodation equally.
If he fails to fulfill your rights then you have the right to ask divorce. Nevertheless, a woman should not resort to divorce unless she compares between the advantages of divorce and the advantages of being patient and continuing her marital life with her husband, especially if she has children from him. Many women rushed to divorce and then regretted it later. See Fataawa 90663, 82988 and 84184.
Moreover, you have to obey your husband if he asks you to come back to his country. You are not allowed to reject his request unless you had conditioned on him when conducting the marriage contract that you will stay in your country, then he is obliged to fulfill this condition. If you choose to stay in your country, then Islamically, he has the right to take the children with him to his country.
It is the right of a wife on her husband to provide her with a separate accommodation even if it is a rented one. She is not obliged to live with her co-wife in the same accommodation.
As regards the condition between you and your husband that if he marries another wife then the flat will be for you and your children; this is a conditional gift, and the scholars have clearly mentioned that a conditional gift is not effective, as a gift can not be conditioned. On the other hand, if you have really participated in building the flat with your husband, then as a principal you deserve your share unless you have waived your right in the flat at the time you participated in building it and he has fully obtained it after that. In this case, you can not take it back unless the gift was for a certain purpose which was not fulfilled.