Is it wrong that I stay on the phone with my clients to make sure I can bill them for extra time spent?
Then you're not being very customer friendly, are you?
I don't care about them, they only care about their money.
It's morally wrong to intentionally waste time with clients so that you can charge them more since you are not performing any extra useful services to them. You should always aim to be efficient with the time that you spend with clients as not everyone can afford large expenses and exorbitant charges will cause financial hardship. It is better to work for the success of your clients and not see them as adversaries since they will become repeat customers and give you more business long term.
I know but I need the money to finance my vacation.
You can't just cheat customers out of money to take vacations. You need to do a better job providing a good service to your customers.