The Sprint MIFI doesn’t have a wired ethernet port, so it can’t even be patched to your wireless router. Not that that would necessarily buy you much, but it’s certainly a non-starter for wired connectivity.
The ONLY possible connectivity here is perhaps repeating. If your wireless router supports configuration as a repeater, then you could extend the Sprint MIFI’s range, but you would also lose access to your current cable/dsl ISP.
Otherwise, I’m not seeing it, at least not w/ your current hardware. These are essentially islands of connectivity, with no visible land bridge between them.