Rob,
I am very familiar with how the old timers make wine, it can be very good...or very bad, it is a crap shot.
I agree with John T, a few books would really help.
You need to get a Hydrometer ASAP.
I'll try to keep it basic, then you can ask questions and we can answer them.
If I understand correctly, you brought the destemmed grapes home, put them in a barrel and and started to punch them down.
You didn't add any yeast, you let the wild yeast ferment them, you pressed the grapes and put the must into 3 demijohns.
Here is a basic how to:
Once you destem and crush the grapes, you put them in a fermenter, take a Starting gravity reading with your hydrometer, or a brix reading, I usually add meta (amount depends on how much you are making) to ward off the wild yeast, You can add various enzymes to help break down the skins if you would like to at this point).
You can let the grapes cold soak (temps must be under 55°) for a few days, up to a few weeks to pull out more color and flavor from the skins if you want to.
Test your PH, TA and SO2 levels, make adjustments before starting fermentation.
Bring the temp back up naturally, hydrate your yeast, pitch the yeast, put a lid on your fermenting vessel.
I recommend punching down the cap (the grapes that come to the top as the level of must increases) several times a day.
When you Gravity level is below 1.000, I prefer as dry as I can get it, .992 -.994 is perfect, remove as much of the grapes skins as you can and press them, be aware that the more you press the more tannic or astringent your wine can become.
Add the juice you got from pressing to the wine in your fermenter, some rack to a carboy or demijohn at this point, others recommend to wait 24 hrs. to let it settle.
Take a Final Gravity reading, with both readings, you can figure out the ABV%.
Rack, stabilize with meta, put a bung and airlock on the demijohn and let it age.
After a month or two, you can rack it off the Lees (sediment), you can do this every few months.
Make sure that you test the SO2 levels and that you top off up to approx an inch below the bung.
The longer it ages, the better it will be.
There are so many things that I left out trying not to give you a data overload, such as: I'd add some oak during the fermenting or aging stage, MLF and a few others.
I'm sure others will chime in as well, I may have left something out.
Let me know if this makes sense to you, ask a billion questions, everyone is really helpful.
Don't try to prove Dad is wrong or that you know how to make a better wine than him, he will never embrace your wine or "new" methods if you approach it that way, why not show him how you make wine, a process that he probably was extremely proud to do with his son, I know that I am extremely proud that my son is making wine with me.
Tom