You can leave the cheap phone plugged in at home all the time and both of you will get any texts that come to the phone. You could set it up to reply to your phone and have it forwarded also.
Someone with the phone number A texts a message to number B. Say the message is forwarded to number C. In order for the user with device C to respond to A, it would first be necessary for B to rewrite the message text to say that the message came from A. They then the user of C needs to make sure to manually send the message to A. Now, depending on how savvy the user of A happens to be, they might not find it completely disorienting. If you were to attempt to send to both A and B via a group text that might help some. But then you'll also be getting extra copies of your messages fed back to you from B. Unless the forwarding on B is also smart enough to filter them. And then there is still the problem that in future conversations, the user of A might just send messages directly to C, bypassing the other forwarding recipients of B, defeating the point of having a shared point of contact.
So forwarding has considerable awkwardness and room for error.
But in any case I think proxying is absolutely possible and would b easy to setup, especially on a rooted phone.
The first thing that comes to mind is setting up a web frontend, so messages would be forwarded to your s and your wifes phones, and then you would access a web frontend hosted on the phone with the $ simcard with a 'real' number which would send out the reply sent via the web form.
Would something like that not work?