I dont want to buy a signal booster because on some occasions I would like to use the router independently too. But is it possible for 1 router to relay the wireless signals of another router ?
Depends on the wireless router.
If the wireless router can be configured to operate in repeater or range expander mode, then the answer is "yes". However most (or maybe all) retail wireless routers do not have this mode; it is a mode offered in some access points (AP).
"Repeater" mode would be one of several configurations if the wireless router was modified by installing alternate firmware like DD-WRT.
And another mode