My DH ‘s son was an adult when we met so there were no issues with taking care of him. But as he is such a POS who was often homeless or in jail needing bail or money to pay a fine to avoid jail I had absolutely no inclination to help him so I didn’t. 

She truly views me as a second mom, unprompted by any of us. I took care of her as a stay at home mom for about the first 7 months that I moved in. He didn't tell me to, I just did it to help. I care about her and I slowly like her more and more as I attempt to shape her into a well functioning person despite her mess of a BM.

But I keep a distance in the way that I don't sacrifice my life or time in any ways that I don't want to. I do things with her that I want. I help when I want. I only spend money on her when I want to. I make plans and she will not get in the way of them. etc. etc.

In the past, I was treated like a babysitter by BM and unintentionally so by SO. I was losing my mind. So I went and got a full time job in September, forcing everyone to get their sh** together. I've never been so happy. 

I think its okay to care about your SKs and treat them like family but you have to be careful that people don't take advantage of your kindness.

Or the grandparent! My XOSD asked me to babysit her daughter when she was a bridesmaid at a wedding. I just assumed kids weren't allowed, and my then DH was working. So, we had a fun girly day together even though I knew then OSD would want detailed feedback. Then, a while after they showed me photos of the day- and there were loads of kids at that wedding- when I said I thought kids weren't allowed they said 'Oh no, we just chose not to take her!' Just another nail in that coffin of my relationship...

The children are the responsibility of the PARENT... period.  If the SO volunteers.. or agrees to watch/care for the children then it is their responsibility to do that task and keep the kids safe during that time.

Now, there are definitely situations where it can become a SP responsibility.  If the agreement is that perhaps the SP stays home to care for the home and the "kids" while the other partner works a demanding job.. then it can become a SP responsibility.  If the SP is given the luxury of being able to stay home with their own kids.. then they may need to take the bitter with the sweet and also be responsible for their partner's kids.  BUT.. again.. this is something that they need to have a mutual understanding on.  Perhaps, if they don't want to watch their partner's kids.. they need to go to work instead because their partner may not be willing to tote all the financial weight if their partner isn't stepping up with the kids.  So.. if you are the SAHM.. consider carefully that it may also involve care and feeding of the kids that aren't yours.  If you don't want to do that fine.. but your partner may not be happy to let you "not work" if they are going to also have to pay someone else to watch their kids.

Otherwise.. it's voluntary.. Now, if I was home and was near a kid and saw them getting ready to do something dangerous.. Obviously.. I would say something.  Even if my partner was home.. I would have because it's a human decency thing.  I also watched his kids at times when he couldn't.. because he also did things for me when I couldn't.. it's normal give and take in a relationship. 

But bottom line, the parents have the ultimate responsibility.. you are not obligated to financially or physically support someone else's child.

Responsibility for parenting them and maintaining their care is the parent.

Responsibility for making sure they don't die is any adult.

If one sees their SK about to fall out an 8th story window, they can't just say "oh well, guess Mom/Dad should be watching closer" as they tumble to their death. There are times when any adult has a responsibility to a child, and those times include any where a child is in danger of their life and/or safety.

There is no set answer for this.

In our home though I am as much of a parent as he is. I share the responsibilities happily. I love the kids and I love our little family.

However, this was my choice. My partner has never demanded these things from me. At this point though it would be a disservice to just stop because we have a way of living that we agree on.

It is the responsibilty of the bio parents, not you. Anything you do for the child is your choosing, not out of obligation. Bio parents are responsible for their child's finances, babysitting, and other responsibilities one hundred percent. No one else should be made to feel guity for doing so.