sounds like your kid was pissing in the sandbox and this poor woman was just standing up for her rights ... well, either that, or she is a very bitter person who lost a lot of karma points at the expense of a 3yo.
regardless. she does have that right. but, if you have been "invited" by another resident of the complex, then you would have the right to be there.
good on you for not arguing and making a bad situation worse for your kid
edit: besides, wouldn't you think anyone who actually contributed to such a large amount of money spent on a playground would want to see it used? it's not like you were taking away space from someone else.