What do I need to do to use steam through 2 routers?

Hi!

I recently posted a similar question to this but did not recieve the answers I wanted. Maybe if I am more clear I can get a better answer! :3

The case is: I recieved a crappy router from my ISP and my internet is required to run through that(it is cemented to the wall). This comes with many problems so I am using my old "Acer FAST" router so that my wifi-signal will be strong and so that I can use other things such as my complicated printer over it. The setup is: Pc - old router - new crap router - internet. (The old router recieves internet from the new one.). This works fine with a few exeptions:

1. I cannot access the steam store, community or profile. Updates and downloads from the library works fine? (ERR CODE 101)
2. I cannot access youtube via typing www.youtube.com in the top text bar but can access it through googling it and pressing the link???(ERROR_CONNECTION_RESET)

What do I do to fix this? Anyone got any idea? Is using the old router as a switch(bridge mode) going to work if I want the functions of that router.

Thanks for any responses!