Coach_Sampson,
Obviously your situation is unique, and not in a good way. 
How do you think having turf will allow both teams to use the same infield?
From the way you worded how you’re planning on justifying the cost, I assume this is a private school.
I’m curious how the field will hold up under the high traffic of access by renting it out. My 1st thought is that’s going to be more of a headache than its worth, but I don’t know. Having done a lot of field maintenance over the years, I can say that there’s a point at which the additional traffic degrades the facilities to the point where it’s not cost effective. The thing about renting is, the renters don’t have the same pride as the owners do and therefore tend not to treat things very well.
Is it at all possible the better answer is what one of our local schools did. Rather than revamp a field that much needed it, they contracted with the locals to use public fields for games, and kept the old field for practices. At the rate they got, it became totally cost ineffective to do the revamp.
I wish you well because I know how difficult it is to provide quality facilities.