What is the ruling of Islamic law on a man who is married to another woman, and then oppresses her and prefers his first wife over her in treatment, lodging, and travel, and does not give her her due?

A husband must be just among his wives, and this is a condition for the permissibility of polygyny. If a husband travels with one of his wives without drawing lots, he commits a sin and must make up the days for the other wife. What your husband is doing by singling out one of his wives for travel without the other is an injustice and impermissible. You should advise him gently and remind him of your right, and you should remind him of the Prophet's (peace be upon him) saying: "Whoever has two wives and inclines to one of them, will come on the Day of Judgment with his side leaning." And his saying: "O Allah, I declare inviolable the rights of the two weak ones: the orphan and the woman."

As for his preventing you from having children, it is impermissible, because it is a shared right between the spouses. We advise you to be patient and not rush to seek divorce, unless the harm to you is great by the continuation of the marriage, with his insistence on depriving you of procreation and not giving you your rights, then divorce is preferable at that time.