The only problem is that the rhythm breaks down in the last line (the bold part).
The lines are stressed 7,7,7,6 (or 5).
It's OK to vary the rhythm a little at the beginning of the line, as in line 3, but having it break down in the last phrase is ... um, terminal.
A possible fix with 7,7,7,7 beats:
Once upon a moonlit night there was a little spider
Who sadly came across a girl who’s name was Molly Snyder.
Poor little guy stood no chance against her platform shoes.
She screamed and cried and smacked and stamped and reduced the spider to ooze.
"Reduced" would be better as single syllable. So would "spider", but I guess you're stuck with it.o would spider