If the husband doesn't pray and doesn't go to the mosque. Does the wife have the right to a divorce?

According to the Shari'ah, only the husband has the right of divorce. The wife does not have the right of divorce.

In your situation, we advise you apply wisdom and make your husband perform Salat and be Shari'ah compliant. Your success will depend on your approach and wisdom behind changing him. There are many women who have successfully changed their husbands and made them adhere to Shari'ah. You should be steadfast and never give up your efforts in achieving your objective. If you feel that informing your husband of your intention to terminate the marriage due to his un-Islamic behaviour may be useful in chaing him, you may try that.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai