I think the problem here is that the parents are expressing a lack of emunas chachomim and are not keeping in line with our mesorah:
First of all, while it may be true (I’ve never heard of this but I can ask my b-i-l who is sephardi and didn’t have this for his daughter) that certain sephardim have some sort of “simachas bat”, I think it was assumed that the parents here were not sephardi. This then is a clear violation of their mesorah. The mesorah is there for a reason, not to cherry pick what we like about it, but to follow. I can’t start putting my tefillin shel yad on while sitting (as sephardim do), simply because I think it is the “better” way. It is not part of my mesorah. A mesorah that was formulated by the talmidei chachamim of my ancestors’generations. Which brings me to my next point.
The halachos of the S”A are not the only place we turn to for deciding how to run our lives. It is the basis, yes, but within the strictures of the S”A we are required to follow our Rabbonim. Those Rabbonim can and do institute further minhagim into our mesorah, such as kitniyos (as was pointed out in another post) and even gebrokts. These reasons make sense to them, and as I am not even a fraction of the talmuch chacham that they are, it is incumbent on me to be mevatel myself to their da’as.
Ashkenaz Rabbonim have not instituted any sort of “simchas bat” and therefor it is not part of our mesorah. By formally ritualizing a practice that was not instituted by our Rabbonim, a person is essentially saying, “Rabbonim, your reasons for not instituting minhag X are invalid in face of my feelings.”
Yes, the birth of a daughter, I can testify to, is a very joyous time. But that doesn’t give us the right or the ability to begin performing rituals that are not part of our mesorah.
I am not expressing my opinion of these people as people. Obviously these are people that feel tremendous gratitude for every gift they are given. However, their actions express how they associate to certain aspects of Judaism. That is not a judgment on them, that the reality that they are manifesting with their actions.