TBH at age 2 your dc will be too likely to wee in the jacuzzi to make it responsible to risk them going in - is worse than weeing in pool as will not be diluted by mass of water.
Once kids have reached 6 or 7, though, I would say it is the complaining old ladies who are more likely to pee in the jacuzzi TBH!
Blanket bans on under 12s are not really to do with any real health risks for kids, more to do with the British intolerance of even well behaved, quiet kids (am assuming you are in UK, OP, though correct me if I am wrong).
When I visited friends in Finland, we went to an aqua park with jacuzzi and steam sauna. Lots of kids in both, it is accepted as normal there. The rule is that they are safe to go in as soon as they are old enough to walk out of the jacuzzi or steam room as soon as they are uncomfortable. I would trust the safety rules of the Finns here, they did after all invent the sauna!
Having enjoyed using jacuzzi and steam room in Finland, it is difficult for my 9yo dd to understand why she cannot use them here. All I can say to her is that it is not fair but that is sadly the rule.
On the one occasion that I let her dip her toes (ONLY her toes!) in the jacuzzi at our local club, within seconds an elderly lady marched up to a member of staff and demanded that she be removed! Crikey, she does not have any infectious diseases!
anyway, I am rambling!
In short, YABU to let such a young child not yet in full control of wees and poos use the jacuzzi, but YANBU to object to the ban of all under 12s.