Frome My point of view their is more thant one answer to your question.
First i would call your client ISP to open the internationnal trafic. their is no reason except for nationnal security to stop internationnal web site. But i’m not in your contry.
second if you want to use a proxy use the proxy.pac file config that way when you clinet move away the browser will not find the proxy.pac file and he will use the default gatway and byepass the proxy setting.
third you can by a more reliable router for SMB. I use SonicWall router. you can configur remote gateway no problem.