What is the ruling of the Shari'ah concerning a husband who caused a woman to be divorced so that he could marry her?

Your husband's relationship with that woman is forbidden by Islamic law. His attempt to make her divorce her husband makes him a "mukhabbib" (one who corrupts a wife against her husband), and he must repent to Allah.

You must advise him and remind him of Allah. If he repents and rectifies his conduct, then you do not have the right to seek a divorce. Otherwise, you do.