I agree about delete the polite if they aren't listening. If there is a roundpen and someone is riding in the arena you should definitely use the roundpen to lunge regardeless fo the age of the horse, but with a green hrose it is much more important.
IMO if I saw someone (esp. pregnant) being led with their child in the arena I would wait unless I was on a very calm horse. I don't like to mess up other people's ride if my horse is being stupid. I'll just give it a few minutes and let them get done. I have never had to ask permissoin, but we were all expected to be aware of what was going on in the arena. If there was a lesson, someone really trying to work their horse alone, etc. we would ride out in the grass, use the roundpen, or just wait for a little while.
I really think that you would be in teh right to bring this up to your BO.