The simple answer is: You reduce a cream sauce the same way you reduce any other sauce, by simmering it until a certain amount of liquid is gone, just like the instructions said. You have to be careful about temperature though, because milk (or cream) can burn at high temperatures, and then your sauce is ruined. You should keep it to a low or at most medium simmer.
Cream sauces normally tend to thicken extremely fast, so the long cooking time is almost certainly due to watering it down. I don't think the water was necessary at all; the chicken broth was probably for flavouring, and although "broth" is a somewhat nebulous term, one would normally expect a broth to contain at least some amount of gelatin, which will cause the sauce to thicken substantially when it cools if you reduce it a lot. Water doesn't, so you've added no flavour and thinned out the sauce.
Basically, you (or your wife) added water for no other purpose than to try to evaporate it later. Water generally doesn't go in a cream sauce. If you don't have chicken broth or can't use it, I would either substitute more wine or just leave it out completely. Usually the only time you substitute water for broth is if it's actually the base of your sauce.
The biggest reason your sauce didn't thicken is that you didn't have much of anything at all in the pan that will gelatinize and help trap the water molecules present in the sauce. Starches (flour, cornstarch) will provide some of this, as will a liquid like stock that contains some dissolved collagens. But wine and water by themselves will have very little thickening power. At minimum, you'll want to add a teaspoon or two of cornstarch to your wine/water mix and shake in a covered vessel - this is called a slurry and will thicken fairly quickly, but you need to be careful not to overcook it.
For a more traditional (and in my opinion, much tastier) pan sauce, try the following steps:
First, make sure that you pour off any excess oil - you want no more than about a tablespoon or so left in the pan, less if you're adding butter.
Second, heat the pan by itself for a few moments, which will help dissolve the fond (little flavorful brown bits left in the pan) during the next steps. If you want to add your onions, this would be the time to do so.
At this point, if you want a really thick sauce, add your butter, and sprinkle in a very small amount (no more than the amount of butter you've added) of regular flour. Whisk this well for about a minute until it seems to thin slightly. What you're doing here is creating a quick roux that will help thicken the final mixture. You can skip this step if you like.
Next, carefully add your wine and wait a moment to help burn off some of the alcohol flavor. Whisk or stir with a fork for few seconds to help dissolve the flavorful fond. Then, add stock - this is very advisable especially if you didn't create a roux. Stock both has more flavor than water and (especially with meat stocks) contains collagen, producing a more velvety-tasting final sauce. Store-bought stocks are fine, and are a great pantry item to keep around; you don't have to make your own.
At this point, stir in your other flavorings (herbs, etc.) and reduce the sauce over medium-low heat until you're happy with the texture. A good way of checking is to dip in a spoon, flip it over, and run your finger across the back. If the sauce doesn't fill in the track left by your finger, it's good to go.
Best Answer
There are a few factors that could effect this:
1) How the meat is cooked and how lean or fatty it is. If you overcook the meat (although I doubt that you would!) or if it's leaner or fattier. If its a fattier meat add say an extra 2 tbsps or so of sauce and if it's leaner (or overcooked) I would add a tbsp or so less of sauce.
2) The viscosity and composition of the sauce. If it's a white wine sauce (thinner, less rich) you would want to add more, however if it's a hollondaise sauce (thicker, richer) you may want less.
3) Opinion, some people like more sauce, some people like less. It may depend on the type of sauce which you may want more or less of.
Saying this I would say around 4 tbsp of sauce, then account for the additions and your own personal preference. Any more sauce and it may become swamped, any less and you will not have enough sauce to taste or keep the meat moist. It is a very subjective subject so do keep that in mind.