It depends in part on whether the nonimmigrant visa you hold actually authorizes you to transit the US. For example, if you hold a G visa, you probably cannot use that to transit the US on a personal trip unless you reside in the US.
Assuming you have a B1 and/or B2 visa, or an actual transit visa, or some other visa that is valid for your present purpose, then if I were you I'd travel on the Honduran passport. You already have the visa, so use it.
I would not worry about using a different country's passport than that your child is using. Bring your child's birth certificate to prove your relationship. Border guards see children traveling with their parents and using different passports all the time. I know this because pretty much every time I travel internationally, I see at least one family with passports from multiple countries (I live in the US, where there are many immigrant families). If I see such a sight at least once in the 10 to 30 minutes I spend in the security line and passport control line, how many times must the passport officers see it in each shift?
If the preceding paragraph did not convince you, you can also bring both your passports (which you should probably do anyway, as you'll want to use your French one to get back into France). If anyone should say, "how can you be this child's mother if you are not French?" you can respond by saying that you are French, and proving it with your other passport. But nobody is going to say that.
Here's a source that should reassure you that, according to the US, you can choose whether to travel on your visa as a Honduran or with ESTA as a Frenchwoman:
Do I need to apply for ESTA if I have dual citizenship from both a VWP country and a non-VWP country?
If you are flying under the terms of the VWP, with your VWP passport, you must apply for ESTA. If you are using your non-VWP country's passport, you will require a visa and therefore ESTA does not apply to you.
Finally, you seem to be aware, but others who find this question might not be, that your decision about which passport to use is essentially independent from the fact that you're traveling with your French-citizen daughter, because she needs an independent ESTA even if you also have one:
Do I need to apply for ESTA if I am traveling with a minor (child under age 18) who is a citizen of a VWP country?
If the minor is traveling to the United States under the VWP as a tourist 90 days or less, he/she is required to obtain an independent ESTA approval.