expanding my empathy towards other cultures and tangibly seeing what this world has to offer has paid dividends in my life
Congratulations on getting out. This is a really tough situation and I have a similar, although not identical, one. I'm the first person in my family to begin to get a professional degree (law school, starting this fall) and I have a relationship with my parents that bounces between "utterly terrible" and "sort of workable." They live in a small, rural town in an extremely religious area. My dad is the alcoholic, not my mom, and I don't have an especially positive relationship with either one. But anyway, I relate to the tone of your question, if not the details. How do you deal with a family whose lifestyle is different from your own, especially when they blame you for having a better life?
I get asked about twice a week if I would go to church, watch this video of their new preacher, consider donating money to the church, etc. The answer to all of these questions is a solid no. I try to be a little more accommodating in other aspects of their lives, but it's hard. My mom is also pilled up to her eyeballs. I judge her a lot for this, and for her childish behavior in general. I try to be nice to her, but talking to someone who hasn't read a book in 20 years (literally, this is not an exaggeration) and whose idea of quality television is celebrity news shows is tough. She's also a hoarder and gets extremely angry with me when I try to clean up parts of their house. Her whole side of the family is choc full of OCD-type illnesses. Her mother -- my grandmother -- is like your version of your dad, she's my best friend and we would do anything for each other.
How is your relationship with your sisters individually? You can at least be a good role model to your nephew, it's not the kid's fault that his mom is a less-than-stellar citizen. I would continue to cut ties with your mom, unless you have a compelling reason not to. Drinking and gambling are not things that you can help her with, other than encouraging her to get help. Overall you don't want someone like that in your life on a regular basis.
You mentioned welfare. It's easy to judge people for this, but some people do not have a basic financial education and managing money is like asking them to learn neurosurgery. (Also, they should really consider getting their GEDs. It's not hard and it will increase their income significantly.) If you could help your sisters with managing their monetary affairs, try to steer them away from terrible boyfriends, and accomplish all of this in a way that is not preachy, I think you could improve your relationship with them. You must share at least a few common interests. And your sister with the kid will appreciate you at least making an effort to see him sometimes.
And I agree with the other poster! Consider dating someone seriously and starting your own family. Grad school is a great place to meet people.