Who is right?

Sethcopp, here is my two cents. I think you have a good plan. As a pitcher versus a position player you need the rest to recuperate and not put UNNESSASARY stress and workload on your arm. Control issues are usually related to mechanics and can be worked on in the fall after you start throwing, regain, add strength and strengthen your core, which is critical. In your month of rest just don't get out of condition. Maintain some sort of cardiovascular work to keep a semblance of conditioning. And lay off the Dorito's!

Seth you have the perfect plan. Give your dad the links to Cressey and driveline's website(s) and let him do some research on his own. Pitching to batters at this point add zero to your development IMO, You (and your dad) will likely be pleasantly surprised with the additional control you will likely develoP getting away from the game and gaining some strength. 

Ask your dad this question. "does practice make perfect?"

Hint the answer is "practice makes permanent" 

Practicing something something over and over without fixing the root  cause will do nothing for you at this point in time. 

Good Luck!

How many innings have you thrown this spring/summer?  How does your arm feel?  What is your current velocity?  You will get tons of opinions here, and there is no right or wrong.  I'd say if you haven't thrown a ton of innings (?? 75 or less??) AND your arm feels good (as in strong and healthy), continuing to compete and battle vs. good competition would be best.  You could schedule a few sessions with P instructor to fix any major mechanical flaws.  Control issues come and go, too...can be mental thing to work through as well.  You should have an arm care program and light, maintenance type lifting program you can do during the week and throw on weekends.  If you want to play in college, this Fall will be important to start to get some exposure.  Should be able to plenty of heavier, off season lifting starting Nov.  Either way can pay dividends down the road if done correctly.  if you were a year younger, I'd feel more comfortable saying take the fall off and work hard on legs, core, etc.  Also depends on your current velo, if it is too low, there is no need to seek exposure to colleges.

I threw probably 65 innings combined spring/summer. Fastball around 75 maybe a little higher but not much.

At 75, I agree with BOF and OMM.  Do a great throwing/arm care program and stretch/yoga and work your legs (explosive movements...squat, dead lift, lunges, hang cleans, etc.) and core like crazy.  All of this assumes you desire to play in college.  To get interest from even DIIIs, you have some wood to chop on the velo side.  It can be done.

Ok! Should I follow the lifting program I mentioned or is there a better one I should look into?

I think it sounds great.  I don't know it well, but I heard nothing but extremely positive things about Cressey.  We are based in the mid atlantic, and my son works with some local guys who do a customized/modified version of cressey, wolforth, etc.  So, I defer.  Good luck and you are to be commended for your initiative.  

Ask your dad: Is the goal to be successful right now? Or to be successful in moving on to the next level?

If the answer is B, your plan is probably better suited for that.

You are more likely to improve control by building a body that is capable of performing a repeatable delivery consistently than by pitching to batters for another month or two at the end of a year in which you had a heavy workload.

I like the general outline of your plan.  If I were to advise any changes, I would suggest taking TWO months instead of one to rest your arm and work on conditioning.

I would advise the rest / conditioning route myself.

Personal experience...  My son (2017) didn't pick up a ball for 3 months due to tendonitis.  He did nothing other than rehab and conditioning.  His first full velocity pitch off a mound was 8 mph higher than he had ever thrown before.

Seth - none of us sit in your shoes.  I suggest format a plan and execute it according to what YOU think is best.  Your plan sounds like a reasonable one to me.

I agree with JH above. It's about the end-game not about what happens next month. You seem to have a good head on your shoulders....best of luck to you.