How can I make tomato soup etc that doesn't break?
Need to know what you are doing.
Most of the time the cause is because of temperature, e.g. adding cream to something that's too hot. Other times it's a combination of heat and acid that will cause dairy products to curdle, this is because the casein proteins in most dairy products are stable to boiling temperatures, but they're sensitive to acidity, and the combination of heat and acid will cause them to curdle.
But without knowing more of what you are doing, it's impossible to say for sure.
Recently I had some heirloom tomatoes that I had cut in pieces and frozen. I took a Zip lock bag of them out of the freezer and heated then up in a pot. When they were hot I poured in some homo milk from the fridge. The milk broke right away. I sliced some Yukon Gold potatoes and sweet onions and poured on some milk and put in the oven to bake. When the potatoes were soft I took the casserole dish out of the oven and the milk had curdled. Things like that.
Well that's your problem right there, right?
Generally, hot liquid (with acidic content) + cold cream = curdling.
Try to temper and have the temps of the two liquids as balanced as possible, or add very little cream at a time and fully integrate it into the sauce before adding a little bit more.
Also, try using something with a really high fat content, like creme fraiche or heavy cream, which has very little to no casein.
Try using a can of Nestle "Table Cream" (aka Nestle "Media Crema, if you buy it in a Hispanic store).
If you have no objection to the emulsifiers in the stuff (natural emulsifiers), this product is tops for making cream soups of any type. I've never had it curdle up no matter how I've used it. A spoonful of it is also great in scrambled eggs.