Run a VNC server on your work phone and a VNC viewer or client on your personal phone. Then you can run your work phone using your personal phone.
I don't see why, if you have both phones available (they'll have to be on the same network unless you want to open a port on the network the work phone is on), you care which keyboard and screen you use to send and receive texts, though. (Texts work by phone number, since they're phone calls as far as the telephone network is concerned, so you can't directly receive a text that's calling one phone on another phone. The phone receiving the text has to be using the phone number that the text is being sent to. Sending a text - the text gets sent from the number of the phone that's sending it.)