Ebeny, come to my NCT group, no problem with 4 year olds (though most admittedly are at playgroup and many mums drop off first, then pick up afterwards.
I can sort of understand the pushchair rule in a crowded hall, but not a half empty one. As someone who runs a drama school if someone wanted to bring a buggy inside (sleeping child etc) I would either offer to babysit myself just outside the hall or remove a chair and slot the buggy in the space, so as not to clog the aisle up.
At my dd's nursery (part of a prep school) I often wheel ds into dd's classroom, in his buggy.
I havn't yet challenged my clinic (its not within walking distnace but where I used to live I took the pram in, (was held inside doctors surgery)it never occured to me that I couldn't.