Having worked in a GP's surgery, my take on this runs kinda like follows:
- Complain about the nurse. She was rude and unprofessional. Yes, you hadn't realised you couldn't have you children with you - so what? Her only acceptable response was:
"I'm terribly sorry but the Doctor won't conduct the procedure with small children in the room. I'm afraid that should have been explained to you."
Followed by
a) We can't fit the coil today, but if you ask at Reception, they'll make another appointment.
OR
b) Let me just ask if there's anyone who'll watch the DC for you.
I agree that Receptionists are often extremely busy and can't be expected to do this, but it happens more often than you'd think and tbh, the staff where I worked were usually only too happy to coo over someone else's kids for a few minutes. It happens with lots of things, even jabs, so I wouldn't stress over that.
Agree that the receptionist would already know why you were there - it would be showing on her booking screen. Appointment lengths vary, are often colour-coded and will have notes as to why the Dr is also booked for a space. So don't worry about that.
I'd focus on the nurse - and possibly on whoever did your initila explanatory session - cause it sounds like they dropped the ball big-style on the info they gave you.
But, seriously, complain! You'd, believe it or not, actually be doing the Practice a favour by highlighting the issue. You would not believe the number of times my Reception team were almost begging patients to compain about things so that something they knew was an issue would finally get dealt with!