I was just wondering, is it standard procedure in a normal delivery...

That's not true.
I am able to somehow schedule office hours as well as stay at my
client's homes from the time that labor is established until after the
birth.

Not only that,...but OBs don't see you after the birth until 6 weeks
postpartum. I come back 1 day after the birth, 3 days aftrer the
birth, 1 week, 3 weeks, and then 6 weeks after the birth.
and still manage to do all my prenatals and birth care.

presumably though you occasionally have to cancel an office hours time, or
have someone else attend for a short time?

My midwife had her clinic 2-4pm on a Tuesday, and it's certainly not going
to be the case that no one ever has a baby at that time! She kindly did all
my prenatals at my home and a couple of times they got moved to later the
same day because other things happened.

Cheers

Anne