You daughter's medicine isn't considered a national security threat. It was not possible for them to confirm what it was, and they decided it best to let you trash it vs taking a chance on your possibly sneaking liquid exposives aboard an airplane. Sorry, but they found that very scenario was going to be used by the terrorists in Britain.
On Sat, I flew and, knowing my meds and such were a potential problem, I put them in my checked luggage. Obviously not everyone had been aware of that resolution, and some require immediate access to the meds. But what else could they do?
If Marshmallow and daughter were not YMMs, then it was terribly stupid to take the Asthma inhaler away for ANY other reason.
And I've fixed your last sentence for you.