In the UK we have 'fortnightly', and instantly get rid of the problem! 'Twice per week' would be the best way of saying what you ment.
I'd only be worried about liability in accidents, both regarding the kids injuring themselves and to anyone else they may injure if this is a public area. You don't want to get sued for a kid knocking over some old man and breaking his hip!
If the parents are all good friends then who is the coach to say that you shouldn't be coaching their kids?
It'd be very different if you were going out into the community and finding 'random' kids from local schools and whatnot - but just explain to the other coach that you are only teaching friends of the family and not in the tennis business if there is an issue. If being reasonable fails, remind the coach that you live in " 'murica, home of the free market" - and threaten an anti-trust case!
A poor man's right handed Verdasco (Wilson Prostaff 95s /w SPPP@50lbs)