The less emphasis you place on who is in the corner during a match the better off your wrestler will be. You make your wrestler better at practice not during a match.
I too support mixing it up by practicing at different places. Our family has belonged to six different clubs over the past 12 wrestling seasons. We never left a single one of them because we were mad but to go where the best practice partners were. I support everyone of these clubs to this day and it really BOTHERS me that some clubs are territorial, possessive, and down right mean about this topic. I have heard stories of HS coaches scolding kids who wrestled for a club other than their local club and that is just down right ridiculous! Open practice is good for your club and for the other clubs too. My boys have been guest partners for WWC when we visit Wichita, Liberal Wrestling Club when we visit Liberal, etc. If you are traveling call the club director and most will invite you in with open arms. To me, the friendships and acquaintances you make over the years as a competitor, coach, parent, support, fan or whatever are the greatest rewards this sport has to offer!
One last thing. As a dad it is SUPER important to realize when your time as a coach has passed. When your wrestler is young he might need you in the corner to give him a hug whether he wins or loses but as they get older they need a coach who isn't a dad (most of the time). A dad should offer unconditional support and love while a coach needs to send be able to push your wrestler "over the wall" or "through the wall". Don't butt heads with your kid, find a good coach to do that for you!
GOOD LUCK TO ALL!
