May I offer a suggestion?
In your shoes, I'd sit downw ith both of them face to face to find out if they really want to change their behavior for the sake of the baby. If the answer is yes, I'd tell them that I will help with this month's bills if and only if they BOTH attend, in person, a Dave Ramsey Financial Peace University 12 week course, do all the course work, etc.
I know very few men who have been through the program who would still justify their behavior eating out every day while their family faces eviction after going through the Dave Ramsey class. He is completely derisive towards men who do that and it convicts the spirit of most.
"Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. This is the first and great commandment." (Matthew 22:37-38)