All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is unlawful for a woman to ask her husband for divorce just because he married a second wife. It is well-known that Allah made it lawful for a man to marry up to four women if he can be just with them and can spend on all of them. Allah Says (what means): {…marry women of your choice, two, or three, or four…} [Quran 4:3]
As for your saying that he doesn't care about you and your children, then we believe that this might be only insinuations from Satan to disunite this family. But if your husband is, in fact, unfair, then he should be admonished and reminded that fairness and justice are pre-conditions to polygamy. So, he should deal fairly and justly with his wives as well as his children.
Similarly, it is forbidden for him to abuse any of the wife's rights. Allah Says (what means): {And live with them in kindness.} [Quran 4:19]
On the other hand, we advise you to be more patient and not to ask for divorce. You should also supplicate Allah to guide your husband to that which is good for you all in this life and in the Hereafter.
Allah knows best.