Matt - If I were you. I'd keep my head down & try to deal with it on board if need be. Latam flight crew are MUCH easier to deal with than Latam ground crew & also many will speak english.
If BA have issued a ticket for your infant, I can't see how Latam can fail to honour it. Whether they charge BA 10% or 100% of the agreed fare for redemption seems to me to be an issue between BA & Latam, not you & Latam.