My wifes Birth Certificate is falling to pieces so we want to renew it

Do we have to go to the Amphur who issued it or can we use a nearer office to where we live?

I'm not sure about that one. An original can only be issued by the amphur where you were born, so she probsably have to go their. But she can try to see if it is possible to get a copy at another amphur.

If not, it might be possible to give someone a power of autorney to get a copy on her behalf.