In your persistence.xml change the line
<persistence-unit name="myPersistenceUnit" transaction-type="JTA">
to
<persistence-unit name="myPersistenceUnit" transaction-type="RESOURCE_LOCAL">
Also it would probably be best if you create a datasource bean in your Spring configuration instead of using implicitly in persistence.xml (that way you can easily switch datasources with Spring profiles)
Check out this tutorial for details
To fix your deployment issues on Glassfish, see this and this link. From those links one suggestion is to set the version in your web.xml to 2.4 and the other suggestion is to do perform a whole bunch of steps to get Spring to actually play with transaction-type="JTA".