I think the simplest solution is to do manual context entries in [TOMCAT_HOME]/server/conf.xml file and define the priorities in there. Lets say if you have two web applications WebApp1 and WebApp2 and you want WebApp1 to load before WebApp2.
Make two entries in [TOMCAT_HOME]/conf/server.xml as shown below:
<Context path=“WebApp1” docBase=“PATH_TO_WEBAPP1” debug=“0”/>
<Context path=“WebApp2” docBase=“PATH_TO_WEBAPP2” debug=“0”/>
The context entry for WebApp1 should come before the entry of WebApp2
Note: Make sure you are not copying any war files for your web application in the webapps directory otherwise this will load up the applicaiton twice because by default the webapps direcotry is configured to be [TOMCAT_HOME]/webapps