You are asking for a lot for $400. My take on this is that meeting all of your needs with OS hardware is probably impossible. Something might be possible if you are willing to give a bit. Here are some thoughts about OS hardware. I don't work for OS or have any association with them other than being a customer. I am familiar with much of their product line. Perhaps others can comment on other brands of hardware...
There is a new internet weather solution here:http://us.oregonscientific.com/cat-Weather-sub-Professional-Weather-Stations-prod-Anywhere-Weather-Kit.html
that gets you rain, wind and one temp/RH sensor and internet connectivity for $200. I have never tried this and don't know much about the internet functionality, but it might be worth a look. Very turn-key and you would be stuck with whatever data format they decide to provide on the internet. You can add more sensors (e.g. THGR810 at $50 a pop) so you could get 1 outdoor and 4 indoor sensors for $400. But there's no outdoor radiation shield for the temp/RH sensor and no indoor displays at all. You can add WMR80 consoles to this for $80 apiece but they will only be able to receive three wireless temp/RH sensors (e.g. one outdoor and two indoor) and you will have blown through the $400 budget limit.
If you can give up your requirement that a PC is not required then more options are available. It's not clear to me what you mean when you say "dedicated PC". If there's a PC involved it would need to be running 24/7 and connected to the internet and OS base console via USB -- but it could be used for other purposes at the same time -- so not "dedicated" in some sense. Again...not sure what you meant by "dedicated".
For example get a WMR80 bundle that includes wind, rain and 3 remote temp/RH sensors for $170. Buy a separate WMR88 console that can plug into a computer (USB) and get some software that can upload the data to internet (e.g. web page, WU, PWS Weather, CWOP, etc). There are several free or pay-for software packages that can do this. Check to be sure, but I think the WMR80 and WMR88 only support three remote temp/RH channels so this would not get you to the three indoor room minimum plus outdoor temp/RH.
To get more channels you would need the WMR100 or WMR200 consoles and I think then you have blown past the $400 spending limit. For example, the basic WMR100N package at $170 includes one outdoor sensor (with a rain shield that performs very poorly as a solar radiation shield, IMHO) and you could add say 3 more sensors for $150 and now you are at $320. Add a WMR80 display and you are again at $400 but the WMR80 cannot receive all of your additional wireless sensors. Add another WMR100 console for $140 and you are way over the budget cap.
I don't know if any of the OS base consoles will automatically cycle between the various remote sensors w/o pushing a button. Perhaps someone else knows?
Finally, this is all very OS-centric and there are other vendors out there...so maybe you could find something better with another brand.