It is truly sad when a husband abandons his family and forsakes his vows. I am very sorry this is happening to you.
Regarding divorce, the Church knows that there can be circumstances where an innocent party is abandoned and divorced against their will. They also recognize that sometimes it is necessary for an innocent party to divorce a spouse to protect themselves and/or children. So, physical separation of the spouses and/or civil divorce, while always tragic and against God’s plan for marriage, can be undertaken in these circumstances.
However, for two baptized Christians remarriage is not possible as long as the spouses are alive. A valid, sacramental marriage is for life. It cannot be dissolved by any power.
That said, what a Catholic tribunal can do is examine evidence to determine if a valid marriage took place at the time of the wedding. There are many reasons that a valid marriage may have appeared to take place but in fact did not.
Adultery is not “grounds” for a decree of nullity (a failure to live up to vows is does not make those vows invalid). But, adultery might be evidence that a person did not intend fidelity or permanence when they made their vows. In other words, it may indicate a defect in consent/intent. But, it may not.
These things are best discussed with a priest and taken one step at a time. You need to take care of you and your children first.
I highly recommend the book **Annulment: The Wedding That Was **by Michael Smith Foster. Read the book to get a good understanding of the Catholic teaching on marriage and nullity.