I wouldn't leave her tied up alone, she sound as though she is scared when tied up. Lots of dogs get stolen when tied up outside shops and other places, so i would leave her in the house if you can't take her in the playground. You would be heartbroken if she was stolen or if she bit someone and had to be pts, so i think you shouldn't put her in that position.

I had a mongrel when I was a kid and my mum used to walk to school with her to meet me, she was the softest, gentlest, well behaved dog you could meet, but as soon as she went near the school, she got really stressed out and tried to pull away,and had a growl at people coming near her. So my mum used to meet me up the road a bit, think it was the volume of kids and adults flooding out the gates that done it, she had never growled at anyone before and never did again