I have a few questions but there are some things you can do without a router. Can you learn if the base installed Belkin, or Netgear or linksys equipment in the hot spots? ( Don't tell ME, you need to know. The fact you did not specifically say Range booster narrows it down.
There are now USB ports that come with a little pedestal so you can stand the antenna upright and point it too. These are the new standard called 802.N ( instead of A, B, or G ) They have in some cases a 3x range. Around $50 online or maybe less at the PX ( what IS the AF term ,,,,BX? )
I'll watch this space for "next steps" Good Luck!