I have been working in an almost identical environment for the last 9 months, with none of the problems you reported. Here are the connection settings for our web app. We use the XML config file, but you should be able to switch these to the properties syntax. Hopefully this'll be enough to get you started.
Code:
<property name="hibernate.connection.datasource">jdbc/your_datasource</property>
<property name="hibernate.show_sql">true</property>
<property name="hibernate.dialect">net.sf.hibernate.dialect.DB2Dialect</property>
<property name="hibernate.transaction.factory_class">net.sf.hibernate.transaction.JTATransactionFactory</property>
<property name="hibernate.transaction.manager_lookup_class">net.sf.hibernate.transaction.WebSphereTransactionManagerLookup</property>
<property name="hibernate.jndi.class">com.ibm.websphere.naming.WsnInitialContextFactory </property>