OK Folks!
I think we are at the end of this. I know I pushed the ends in all the way when I assembled everything. After having sat down and thought the whole situation over it was back to Lowe's. I bought some water stopping tape as a last resort. But! I also bought another union and a tool to take these apart. One is the half moon plastic one that Rene T mentioned. They make another that looks like tongs made of steel. I bought that one. I was able to get that tool in there, and with great effort, I was able to break the connection and from there it was easier to get the old union out of there. After checking for burrs on both tubes I fitted the new union into the mix. After sending some silent prayers to the good Lord above I turned the water back on.
It has been an hour now and no leaks. Leave it to me to find the only defective union in the entire store!! I won't let my guard down just yet but I think this nightmare is coming to an end. Now just waiting for the water pump to arrive for the washer and I can put this whole mess to bed!
I want to thank all of you for the help and words of encouragement to get me through this.