Hi, Renee. This sounds really frustrating.
We just had a similar thread on the WP.org forums, and the culprit there was another plugin that set up a script that plays with the datepicker but didn’t constrain it to only their admin pages. Here it is, in case it’s of interest: http://wordpress.org/support/topic/new-entries-changing-date-to-111970?replies=9#post-4665992
So, my advice would be to try disabling your other plugins one by one until you determine which is the culprit. Once there, you’re probably best off getting in touch with that plugin’s developer. If you’d like help once you’re having a conversation with them, we’re happy to answer any questions they may have.
Hope that helps!