That's pretty cool. I have doubts about a possible house finch/goldfinch pairing or mating. While they are both finches--they aren't all that closely related. A quick search on such hybrids didn't turn up anything.
Perhaps you are referring to the different egg---for instance perhaps a goldfinch laid an egg in a housefinch nest. Stranger things have happened but the traditional nest parasite here in KS is the cowbird. That oddball egg has all the markings of a cowbird.
Here's a photo of housefinch eggs:
www.scienceviews.com/photo/library/SIA0566.html
btw, that first chick looks a whole lot like a cowbird. Momma house finch has her work cut out for her.