So of course it takes some time for the Mars colony to be at an appreciable enough size to be viable as an Earth backup. But once it is there, the colony would be have the incentive to start Earth back on the path to being support for Mars.
Sorry, but again - so would everyone on Earth, to the same extent. And if some on Earth would be unwilling to share resources and information with each other, they would have even less reason to trust Mars.
