M.S.
First, I personally don't think anyone should sit in judgment of J. for asking for some advice. I don't think any of us are the perfect parents or kids for that matter, so until you have walked a mile in J.'s shoes, I don't think it is fair to judge her, her lifestyle or make assumptions about how responsible of a parent she might be or whether or not she is fit at all. There are lots of single parents in this world and the majority are good, hardworking, decent people just trying to do what is best for their kids while not losing their sanity. If J. didn't care about her kids, then my guess is that she wouldn't be trying to make a better life by bettering herself through education or worrying about making sure their is a DD around at the end of the night. Everyone has their own way of dealing with things, and while turning to the bottle is not a way, I don't think going out and having fun signals a drinking problem. From what I read, I don't see that she is saying she is going off and leaving her kids with her parents while she goes out and parties like a rock star. What I did read is that she and her parents have an agreement that she could go out on weekends when the kids are with their father and that the parents are not built in babysitters. So, I'm going to assume that she is holding up to her end of the bargain and not just running off and leaving the kids with grandma and grandpa while she goes out all the time.
Moving back in with your parents can be difficult at any age once you have lived on your own, had your own house, a marriage, kids, etc. My best advice would be sit down and talk with your parents again, maybe take one of those nights when the kids are away and spend it with them--take them out or cook them a nice dinner to let them know how much you appreciate what they are doing for you. Remember, they probably got pretty used to it just being the two of them, so maybe buy them an evening out, while you stay home alone while the kids are away and just have some "me time" once a month. If you are going out, revert back to when you were a kid and your parents knew who you were going out with and where you were going. If you aren't going to make it home that evening, call. Tell them that you will call to let them know that you are safe and let them know where you are in case they need to reach you. I know this is the day and age of cell phones, but they aren't flawless and my guess is your parents would like to have a back-up plan in case they can't reach your cell for some reason and need to if one of the kids is sick or hurt. As someone else suggested, at the beginning of the night see if the DD is willing to drive you home, if not, find someone that is or consider being the DD yourself, pace yourself and cut off the fun early enough to be able to drive. Another option is Care Cab, it's a free cab ride home. Program the number into your phone so you always have the option.
I guess last but not least is just make sure that you are showing your parents the respect that you expect back. I know it's hard for you as an adult to live back under their roof, but like I said, it may not be as easy as you think for them either. Part of the problem may be that they see you out on weekends and them wondering about whether or not you are saving any money for the future. Make sure they are aware of your savings plan and make sure you have one.
Good luck,
~M.