MY husband left 4 days ago , is gainfully employed and refuses to pay child support. The home we lived in has attatched rental property,I did own this before we married.Can I file Abandonment charges?

I owned my home before we married and my husband left 4 days ago, does he have any right to the reduction of mortgage that occurred in the 9 yrs we were married?

No, First there is no such thing as filing abandonment charges when a spouse leaves. You file for divorce and, maybe, use abandonment as grounds. But with most states having no fault divorces, that may not be necessary. Besides, I doubt if the courts would even consider abandonment as grounds for 6 months.

Second, is your husband on the deed to the property? If not, he may not be entitled to anything.

Finally, I really don't understand when the custodial parent says the NCP "refuses" to pay child support. Its not their choice! The courts will require it. So you file for divorce, and ask for emergency support. If he is "gainfully employed", his salary will be garnished for the support.