Crossover tube

I need some expertise advice. This is a part neither I or anyone I known has ever heard of. My husband was always my go to on car issues and since that is no longer possible I have my 2 sons (neither are mechanics) and you people. My car was acting fine, then all of a sudden one evening, the temp gauge basically exploded up to the H. It hadnt had time to overheat. After 3 days of doing this I took it to my local Chevy dealers. They said the seals and gaskets on the crossover tribe had gone bad. $320 and 2 days later I got my car back. The first drive was a trip 60 miles away. No problem. The next morning I get about 5 miles from where I was staying I was stopped at a light and noticed steam coming from under hood. I went to local Chevy shop and they said they couldn't find an active leak but antifreeze was coming from somewhere. I got back to town and took car in thinking maybe they didn't get something quite right. Now they say its the water pump and will be another $285. Shouldn't they have checked water pump first? Am I being bilked? Im on disability and there's not a lot of extra money to spread around. Any ideas would be greatly appreciated

Year and size of motor..Probably a 3.8 and the two elbows that run from the idler assy were replaced... The Stealership really isn't going to be the smartest move when getting repairs. Most charge $85 and up for 1 hr labor rate. How many miles on the car