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 most accurate substitution would simply be rum extract. It is concentrated rum with a huge kick of flavor, and much less alcohol. A little goes a long way.
If you're going to stick with a strong liquor my first choice would be a bourbon, it's a similarly "sweet" liquor that tastes good in baking. Another good option would be cachaça.
If you're avoiding liquor, then you may be able to use vanilla extract. Non-alcoholic varieties are available. According to Ochef you can also use molasses thinned with pineapple juice.
The rum is used simply for flavor.
Best Answer
When I am substituting in a recipe, I usually use coconut cream instead of cream or half and half if called for in a recipe. (There is a question posted here that covers how to get the cream from a can of coconut milk.) Sometimes I use soy creamer, but sometimes that can be hard to find. I'm sure you could experiment with a mix of soy creamer and soy milk.
My ideal solution is to use vegan recipes to start with, because they are formulated without milk or eggs. Maybe in your case, just look up dairy free cake recipes, if you don't mind eating eggs. There are a lot of cookbooks and blogs out there with a ton of vegan cake and dessert recipes.