Unfortunately you can not uninstall Google play that easy, but luckily their isn't a need for that!
Google play may stop working due to;
Not enough memory on your device,
Your Date and time may be inaccurate.
I suggest checking both of these things, Another thing you can try doing is opening up your settings, applications, Application's Manager, Find Google Play. Their should be a 'delete cache' button. This deletes any miscellaneous properties and will not cause any harm. Once doing so go ahead and restart your phone and try it.
Hope this helps :)
If that doesn't work, their is a clear data button, this removes your account info etc off Google play, But can be re-instated back on once you open up Google play again.
Now their is also a uninstall updates button, this restores the application back to its default factory settings. You could do this and go into the old version of Google and it should update itself.
Hope it helps!