flushing a heater core

update:
This poor car was mistreated for a long long time. I flushed the cooling system and took the water pump apart. The water pump was so chocked full of crap, it amazes me that it even turned! For now, I am bypassing the heatercore, as I decided to forgo getting a new one. ( i had to make an unexpected long trip and need the gas money).

After idling, it would start steaming hot anitfreeze out of the intake line going into the core (coming off of the block). Then the inside of the car filled up with steam and we have a problem :(

I am still amazed at how much crap this car has taken over the last 41 years, 310,000 miles, 10 years in a junkyard and it still runs! I got the car seven months ago, and the last time it had an oil change was 1977. that first oil change was a mess!