Yes, you can often do this substitution and I've done it successfully many times when I've run out of milk unexpectedly, but you should know that the substitution is never going to be perfect.
On a purely mathematical basis, let's say your heavy cream is 36% M.F. You need partially-skimmed 2% milk for your recipe. If you go purely by weight (which is almost 1:1 for volume when talking about mostly water), then 250 mL of 2% milk will contain about 5 g of milk fat. To get that from 36% cream, you only need about 14 mL, or approximately 3 teaspoons of cream. (Note - don't do this, read on!)
Of course, diluting cream at a ratio of 15:1 is ridiculous and you'll end up with something that's just really watery, and that's because milk is more than just water and fat. I only provide the above calculation for illustrative purposes, to show why there's no hard rule or even rule of thumb for this particular substitution.
With normal cream, most people go with half water, half cream, or if they're trying to approximate skim milk then maybe 1 part cream to 2 parts water. If you have double cream, I would probably use 1 part cream to 3 or 4 parts water; that will give you a reasonable approximation of the consistency of whole or skim milk without making it too watery.
Please keep in mind that different recipes/preparations use milk for different reasons, so this isn't going to work everywhere. I certainly wouldn't do it in baking, but for many stovetop recipes, the main purpose of the milk is just moisture, so you're fine to substitute cream + water and it doesn't really matter if you're "exact" - which you can't be anyway.
The curdling effect is produced both by alcohol and acidity.
The alcoholic part is solved pre-heating the wine for a while until most alcohol evaporates.
The acidic reaction is a little more difficult to stop: As wine canonically has 3g/l TA (total acidity), a little Potassium Carbonate (KCO3) will neuter the thing. Experiment from 1 to 3g/l depending on your wine. Filter with care the resulting liquid as it may contain little crystals.
Always remember to pour the wine on the sauce and never the sauce on the wine (not a joke, the milk will curdle instantly).
Some related material and here
You may also try to avoid curdling by adding only small quantities of low alcoholic content and low acidity preheated wine only.
Best Answer
You may have been served Bearnaise, which is a common red meat sauce. Bearnaise is based on Hollandaise (a mother sauce), a butter based sauce. Hollandaise is somewhat advanced to make because it is important to keep the temperature right and the ratios correct while making it, but the result is worth the effort.