Sorry to jump in here. Answering this as a midwife, hoping to shed a bit of light.
Midwives can give Entonox as a midwives exemption but only when the woman is in established labour (at least 4cm). Personally, if you were contracting 3:10, I would have advised you to stay in and offered pain relief, but obviously cannot comment on your individual case as I wasn't there. As the OP said, we often encourage women to ease off the entonox during the pushing stage as it can make pushing less effective. That being said, if the woman is pushing well and baby is coping, there's no reason to take it away.
Regarding breech births, they have become less and less common in this country and as a result, lots of midwives and obstetricians have lost confidence in facilitating vaginal breech deliveries. That being said, I always discuss the option with women if their babies are breech, as some women don't realise that a vaginal delivery is even an option if baby is breech. As a student, I attended 3 breech deliveries (2 sets of twins, 1 cephalic and 1 breech - both breeches delivered but an obstetrician in theatre, and 1 in a regular delivery room). At the trust I work at, we're very lucky to have several internationally trained midwives who are extremely competent and experienced in managing breech births so maybe that's why I have witnessed it.