As a senior citizen who is on a fixed income myself, I do so feel badly for you but experience is indeed, the best teacher and sometimes, "going overboard" in preparation can pay huge dividends.
When the wife and I took our first cruise in '06, we had no benefit of a local travel agent as a gentleman in New Jersey was making a group booking of which we were part. I therefore had to myself insure that all "i'"s were dotted and "t's" were crossed. Throughout the process, my wife thought I was probably an "hysterical Annie" as she couldn't understand why in the world I was getting so technical. As it turned out I wasn't "technical" enough in preparation for applying for our passports (or, in this instance, could I have reasonably been expected to have been).
Nowhere on my original document (nor did it state in government passport requirements that such was indeed a requirement) that while my birth certificate had a raised seal, did it state that the document was "on file" in the state in which I was born (although it was); (something they didn't put on birth certificates back then in the city in which I was born). When I applied for my passport my brth certifcate was refused for that reaon. I thought the requirement a bit ludicrous but I should have known better having spent a career as a uniformed police intructor for a major state department in the Northeast and understanding how ridiculous beauracracy can get. Nevertheless, it was not accepted as sufficient for a passport by the government representative even though it was "exactly" what was allegedly required for a passport by that same US government. I assure you that a large number of folks who have responded to this posting didn't know that, if only because many have been born since they began putting that info on birth certificates. Had I not got my passport and had expected to use that document on boarding, I too may have been refused boarding and remember, things weren't as sticky as even as recently as two years ago.
Believe me I commisserate wth you that the individual who informed you that your child's birth certificate would suffice and when you produced the required document, it turned out to be unacceptable you were understandably incensed. Nonetheless, it was really not the fault even of the representative who declined the document, just as it was not the fault of the Passport representative who informed me that although I produced the document listed by the government as proof of birth, it too was not acceptable. I wouldn't be surprised to learn that your T/A is not listed as being professionally trained specially trained by the industry in booking cruises and the requirements associated therewith. There are many that aren't.
As long as you have learned from your experience just how technical such things can be in this day and age, you have gained from the experience. I also assure you that I and undoubtedly everyone who has responded your post, wish you only the best and that you eventually are able to take your cruise which I am sure you, as have millions of others, will eventually classify as one of the most magical vacations of your lives.