Also let go of obsessing over what Biomom might or might not tell a coach.
I think all coaches know that most parents and adult beginners say untrue things about their riding ability either innocently or on purpose. Mostly it goes the other way, claiming kid is advanced, needs to jump 3 feet, whatever. But all coaches just suspend judgement and watch the rider. If it’s clear kiddo can already ride a bit they may say just kindly and politely, you must have been in lessons already. And kiddo will probably reply truthfully at that point.
Most English lesson programs have safety standards, boots and helmet usually being part of the insurance requirements. Some programs have loaner helmets.
Just let this play out and don’t let it disrupt her lessons on your time.