Yes, most of the Hatches out here do have a common ancestor. Though I'm not from Utah and neither is my dad. Still, it is quite possible we're distantly related.
Wine can add quite a bit to a dish. As to substitutes the first thing to understand, IMO, is that there are dishes where no substitution is possible.
The wine/alcohol is the key flavor for the dish. Veal/chicken Marsala is a dish where you can't substitute for example.
Wine reduction sauces don't generally work with substitutes.
You can buy de-alcoholized wine and they work well though you don't have a broad selection. Still, you can get a lot of the right flavors for basic red and white wine cooking.
Substitution in desserts is very tricky, often not possible, and I can't guide you there.
Many savory dishes can be made satisfactorily without wine. This is not to say they taste identical to the same dish made with wine but are good in their own right.
When you substitute for wine you have to choose your substitution based on these principles:
Volume: If you're adding more than a splash/couple tablespoons into a sauce or marinade, you probably need to replace the missing liquid so the dish cooks properly to a similar consistency. In many dishes, chicken stock is a sufficient replacement.
Texture: Wine thickens as it reduces. Stock usually is sufficient in this department, but you may need to work with other texture elements, maybe a bit of flour or cornstarch or a sugar/honey if sweetness is also part of the final flavor.
Taste: Wine brings some sweetness, acidity and other flavors to a dish.
Acidity is often replicated with a LITTLE (or combination) of the following: lemon juice, verjus, vinegar of the same type as the alcohol (wine, sherry, champagne...)
Fruity flavors come from fruit juices. DO NOT use equal amounts of fruit juice to wine as it will be too sweet. But apple and white and purple grape juices are useful in small amounts. Some of the cranberry juices/cocktails are useful too.
Floral tones are usually ignored but a drop of rosewater might prove useful.
Tannins are generally ignored in substitution.
My basic wine substitition is a splash of apple juice for fruity sweetness, some stock for body and most of the liquid and a squeeze of lemon at the end for acidity and fruitiness.
For red wines, I substitute as above except for some balsamic or a good red wine vinegar instead of the lemon juice.