Unless there was sugar in your cream, there's nothing particularly sweet about this combination. Did you salt the pasta water to roughly seawater saltiness? If not, did you adjust salt before serving? If your pasta water was under-salted, that would explain the sweetness, since the only significant source of salt otherwise was the parmesan.
Heavy cream is equivalent to 36-40% whipping cream.
In the event that your cream was pre-sweetened, there's not much you could do except add salt and hope the sugar doesn't overwhelm. It's a fairly common technique to add sugar to a salty dish to make it taste richer, or salt to a sweet dish for a similar purpose. But it wouldn't work very well if the cream was very sweet. Since I've never seen sweetened whipped cream except in aerosol dispensers, I can't say for sure.
Sunflower lecithin (sorry, best link I could find) is gaining in popularity as an alternative to soy lecithin because it is widely perceived to have a neutral taste and actually has superior emulsifying properties. It's a little on the expensive side, though.
Soy lecithin by itself doesn't taste horrible if you buy it as a food additive (as opposed to a nutritional supplement). It's common to find in a lot of popular frozen pasta-and-sauce dishes, such as Michelina's, which obviously must be microwaveable without the sauce curdling or separating.
Another option is Sodium Stearoyl Lactylate, if you can get hold of it. This one adds a little sweetness which is generally pleasant-tasting, or at least inoffensive. You'll find it used most often as a dough conditioner or in baked goods, but another popular use for it is in commercial sauces, although unfortunately I can't find specific examples right now.
But probably the best emulsifier for what you're trying to do here is xanthan gum. It's also used as a gelling agent, but in small quantities works as just an emulsifier. You can find it, for example, in this Bertolli Creamy Alfredo Pasta Sauce - exactly the sort of thing you're making. It's also used in the Stouffer's Alfredo sauce.
Mix in a little lecithin or xanthan gum as an emulsifier while the sauce is fresh or cooking and it's very unlikely that your sauce will separate, either in the fridge or in the microwave.
As for what you can do to specifically prevent separation while reheating, if you didn't add any emulsifiers in the first place... I really don't think there's anything you can do. If you're a slow enough eater the sauce will eventually separate right in front of you; that's just what happens when you have water and fat in the same sauce. Best to reheat on the stove top in that case, and stir frequently to prevent any further separation.
Best Answer
Emulsions aren't necessarily all about oil vs. water. Alfredo sauce is actually an emulsion of cream and butter, both of which contain varying amounts of both water and fat, and in many cases, if you bought them from a supermarket rather than a farm, also a fair amount of emulsifiers.
Any emulsion is going to be temperamental and not respond well to sudden changes in dispersion. The most important thing to do with one is incorporate new ingredients slowly! If you just dump in a bunch of watery tomatoes, or anything else with enough liquid (water or fat), it's almost certainly going to separate.
Even if you incorporate very slowly and thoroughly, if you upset the balance too much, it might still break. There's no way to know the exact amount you can add without experimenting, unless somebody else has already documented it (not likely).
Sometimes, if your emulsion just creams (see my related answer about mayonnaise), you can restore it to its former glory with sufficient agitation. If it's actually broken then you're in trouble.
Anyway, my advice to you would be - if you want a rosé sauce, then make a rosé sauce, don't waste a lot of time and perfectly good Reggiano cheese trying to start from an Alfredo recipe. I've made a great many tomato and/or pesto cream sauces and the general rule with these (including Alfredo) is that you always start with any oil and vegetables (garlic, tomatoes/paste, etc.), then add your seasonings, then add the cream and slowly reduce it. You don't need or want butter at this point, its flavour will be completely overwhelmed by the other ingredients and it therefore just adds instability.
You might also want to consider using sun-dried tomatoes for a stabler and probably tastier result; they essentially classify as a solid as far as emulsions are concerned, so it's not much different from incorporating pepper or dried herbs. You could just make a regular pesto cream sauce and whisk in some sun-dried tomatoes near the end.