I relate to you a lot. I started out with my dad 4 years ago. Eventually we had to split. I was younger so I had the energy to work the 9 hour day mowing, then go pass out flyers a couple hours, and make sure our books were up to date when I got home. My dad also is to old for the landscaping side of things,he pretty much rides the mower, which he is awesome at. It we tough when we split, his pride was hurt, I cried, we didnt talk for months. Then, as men do, we kind of got over it, he needed work so he started helping me out, and now he works for me as a crew leader. Of course he is a glorified crew leader who makes $18 an hour and doesnt get orders like the other guys. We are both a lot happier with this arrangement than the tension we had before. At first my dad was co-owner because our dynamic as father and son made it weird for him to be an employee and he helped out financially in the beginning.
At some point I had to realize I had my own family, and I needed to make business decisions that were going to best take care of my wife, and now my wife and son.
I am not by any means saying you need to split from your father. That could be a terrible thing for you and your busniess. I have no idea what the dynamic is with you guys and being able to work with your dad is a blessing. I just know I took on to much stress at one point with my father and what we really needed was a dynamic shift.
As for push mowers, I agree with what was said before. If we cant cut it with a 36" walk behind, its worth the time or energy.