If you're boiling something rapidly, and it's not in a terribly deep, narrow pot, then essentially all of the heat output of the burner is going into turning water into steam. The latent heat of vaporization of water is 2260 kJ/kg, so if you want to reduce something by a volume V, and your stove has power P, the time required is:
t = V * (1 g/mL) * (2260 J/g) / P
If V happens to be in mL, and P is in W (J/s):
t (s) = V / P * 2260
This would be modified slightly if you're using a really tall, skinny pot, since the convection within the pot, from the bottom to the top of the liquid, would be less efficient, with more heat transferred to the sides of the pot and out into the air, but I doubt you're actually going to try to reduce something like that. The P here is the effective power; for example, a gas burner wastes a lot of heat out the sides, so the advertised power will be higher. See TFD's answer for approximate efficiencies.
If you don't know the power of your stove, in all honesty, the easiest way to measure it would probably be to just see how long it takes to boil away a given volume of water, and work backwards. To get an accurate result, you should not boil a pot dry - once the water is a thin enough layer, the heat transfer might start working differently, with the pot itself heating up more, and water splattering. So you could, for example, put in a liter of water, boil away at the stove setting you intend to measure until it's substantially reduced in volume, record the time, then pour it out to measure how much you boiled away. At this point, knowing the power output might be overkill, though; you can really just measure the time per volume reduction, and use that, unless you care about the power for other reasons.
Trying to deduce the power of the stove from, say, the temperature of an empty pot or of the burner without a pot on it (assuming it's electric) would be difficult; you'd have to deal with the heat transfer between metal and air, and the convection in the air.
Dependence on ingredients shouldn't be significant - you're still just boiling water, unless there's a substantial amount of alcohol, in which case the latent heat of vaporization will be different. Pure alcohol has a latent heat of vaporization of 841 kJ/kg; I haven't found a good table for mixtures.
For solutions, as I noted in the comments, the latent heat of vaporization should be that of water, plus/minus the heat of solution of the solutes (I forget which direction that's measured in). The most common solutes are probably salt and sugar, which have heats of solution of 70 and 16 J/g, respectively. (I found this table, and converted.) The next most common thing I could think of that might be present in substantial concentrations is citric acid; this paper reports a heat of solution of -57 J/g. In all these cases it's small compared to the latent heat of vaporization of water, so pretending the liquid is water should be a good approximation. It's possible that things change if you're reducing really far: heat of solution does depend on concentration. That is, things are different thermodynamically (statistical mechanically?) in a nearly-saturated sugar syrup than in slightly sweet water.
Alcohol Sugar Fat. Your recipe needs to be more of those and less of water; just like an ice cream.
I had luck with agave syrup as a base (maple or cornsyrup?) that I tested by freezing; when I was satisfied by my choice, I melted in chocolate and additional fat (good coconut oil I think).
Certainly won't be fudgy outside of freezer so finding a recipe is tricky...
Have a look also at that ice cream topping chocolate hard-shell. It has a super low melting point with its high fat content. Wouldn't take much more sugar in the form of a syrup to make it fudgy.
Best Answer
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.