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 exalt his mention as well as that of his family and all his companions.
There are some conditions for a marriage contract to be valid, and if these conditions are met, the marriage contract is valid; these conditions are mentioned in Fatwa 83629.
The guardian of the woman should choose a pious and righteous man for his daughter, as such a man will most likely not wrong his wife. If a husband has two wives, he is obliged to be just between them even if they are in two different countries; this is the most preponderant opinion of the scholars among whom is Ibn Qudaamah. He should be just between them according to his ability, like a week for each, or a month for each and so forth; this is in general. For more benefit, please refer to Fataawa 85002 and 81469.
As regards the law of the country which you mentioned, and the consequences which one could face if he fails to abide by them, then this is a matter in which we do not indulge, rather this question should be asked to the persons concerned in that country who may be able to help you.
With regard to the marriage of your daughter to this man in the situation mentioned, we think that she should not marry him, as she might face some harm and difficulties, and it is better to be on the safe side, this is besides the fact that, she is not pleased to be a second wife.
Allaah Knows best.