I think this question is the type of oddly personal question that doesn't get asked unless people are strangers. If you think about it, a conversation with an adult at a playground with children is very likely to include the phrase "my daughter" or "mama" or some such indicator of relationship within a pretty short period of time. If two adults are chatting at the swings, they will likely know pretty quickly how the children are related to the other adult without having to ask.
If there is a legitimate reason to need to ask that question (like a child who is hurt and an unrelated adult is looking for a parent or caretaker), it's not offensive. There is a reason to ask it, and no reason to assume that the stranger would have any way to know the answer.
At the very least, this type of question shouldn't be a conversation opener. The people who start off with this question often do so because they either don't think you are the parent, or don't think you should be. Your race is too different, you're too young, you're too poor...whatever. It communicates a value judgment more than it communicates genuine interest in the answer.
And while I don't think a stranger can be expected to see that the writer is treating her children as a mother would after just a few minutes observation, I do think it's entirely reasonable to expect someone who has been standing around talking with her for a few minutes to see it. And to expect someone just observing her to keep their questions and their opinions to themselves so she doesn't have to deal with them.
Ultimately, I don't think anyone should be expected to satisfy another person's idle curiosity. If I strike up a conversation with a woman at a playground while we push our children on swings, it doesn't particularly matter whether the children are biologically related to her or not, because I'm likely only ever going to see her when we are both at the playground. If the relationship changes to one that is less superficial, a) I probably wouldn't need to ask if the children in question were hers (because I'd probably have figured out the relationship), and b) if for some reason I did have to ask if the children were hers, it would be far more clear that it wasn't just idle curiosity, and was instead genuine interest in her life.