Heater Core replacement on a Blazer is just a plain bitch, there is just no way around it.
You will have to grunt and piss to get it out but once it is fixed, they rarely ever go again.
What you are seeing is a lack of cooling system maintenance that has turned the Dexcool into a corrosive slurry and you should get the cooling system triple acid reverse flushed or the problem will occur again.
Please take a look at this professioanl article on Dexcool and how the Rad Cap replacement will save you 100s or maybe 1000s in repairs. Air getting into the system via a poor or worn out cap will cause the sludge seeing air will break down dexcool.
http://www.imcool.com/articles/antif...l-macs2001.htm
Your 1998 Blazer is about due for a couple problems are does every vehicle at that age range. Don't be discouraged, it is a good truck and should be very dependable 90% of the time.