Thanks all for giving me some info on the spider. After I had posted the post, I did sit there and ask it what it wanted. Alas, I got no answer back. LOL. But I don't know anymore...

After I left the park and went home, I started to take down some clothes off our clothesline and guess what!? There was another spider! But it was hanging on a shirt of mine. I thought for a moment that the Park Spider caught a ride home with me, but after looking at it... I saw that it had an orange dot instead of a white dot on the back of it. Other than that it looked exactly alike.

But I put the new one in a jar in hopes that I could learn something from it (and not kill it by accident).