In case you want to use Tomcat your only option to share Spring context is to setup just one WebApplicaiton (initialized by WebApplicationInitializer). Of course you can still have separate modules (aka jars) with own @Configuration classes, but these configurations have to be merged in web application.
It would be more flexible if you decide to use EAR packaging. Then you can have still two separate WAR's depending on core and backend services. Then core and backend services can be shared as a parent Spring context (by using beanRefContext) and two war's (frontend A and frontend B) will extend this context