Let's get practical
Awhile ago (a few years?) on TUG there was a discussion of something along these lines, family members who seemed to be taking advantage of others..... If I recall correctly, there were some practical suggestions there of how to deal with it.
I believe those suggestions involved sitting down and mapping out expectations as well as ways to deal with them and a timetable for dealing with them. This set a plan for a transition toward responsibility.
The agreed on expectations need to be written down with everyone's signature or initials indicating acceptance (if not agreement). There also should be some leeway recognizing that the items are subject to change with everyone's agreement.
For example,
You are legally an adult, and have created a child who is your responsibility.
You will need to have a job for at least xx hours a week. While you are working, I will care for the child. Otherwise, the child is your responsibility. If you are planning to go out in the evening you may pay a babysitter; I might (or might not) be that babysitter.
Day care costs about $xxx per week. You will need to contribute $yy toward the cost of day care in my house.
I will provide a home for you and the child, however as you are 1/3 (or whatever) of this family, I expect you to contribute toward 1/3 of the cost of running the household. (or 1/3 of your pay etc.) This will help cover costs of utilities, food, rent/mortgage, etc.
I expect you to pay the costs of your and your child's medical expenses, clothes, and personal items. If there is no father or child support in the picture, I will help you find the appropriate agency(ies) to get child support. That child support is for the child's support, and will go to the costs of food, clothing, etc for the child.
I will baby sit for xx hours a week if you are in school or working. The rest of the time you are responsible for your child or you may pay for a babysitter or day care center.
etc etc....gas, car, phone, internet, cable.....
You will need to figure out a budget. I will help you with this; there are online sites we can use.
You will need to start looking for an apartment. I will help.....
Let's work toward this as an approximate timetable:
You should be able to be on your own by (3 months? 6 months?)
You should apply for xxx jobs per day, with the goal of having a job by yyy
Once you have a job, you will need to look for zzz apartments per day, with the goal of.....
etc.
PJ