Here's a formula that works for your example no matter what your locale settings are:
=TEXT(DATE(MID(A1,7,2),LEFT(A1,2),MID(A1,4,2)),"dd-mmm-yy") & " to " & TEXT(DATE(RIGHT(A1,2),MID(A1,13,2),MID(A1,16,2)),"dd-mmm-yy")
Here's one that works no matter what's in between the dates so long as the dates are of the format mm/dd/yy and at the very beginning and end:
=TEXT(DATE(MID(A1,7,2),LEFT(A1,2),MID(A1,4,2)),"dd-mmm-yy") & MID(A1,9,LEN(A1)-16) & TEXT(DATE(RIGHT(A1,2),MID(A1,LEN(A1)-7,2),MID(A1,LEN(A1)-4,2)),"dd-mmm-yy")
Depending on your situation, this other option may or may not be helpful. You can change the default date format for the system. That affects Excel's date functions so that they will expect dates to be in that format. Once done, you can use the DATEVALUE function just fine. If this is a one-time operation, I'd suggest changing the format, running the formulas, and changing it back. Otherwise, I'd go with a formula approach. You can get all the details of how to change the system settings here. (I didn't copy and paste it all because it's long.)