Our international travel was always after the kids were able to carry on a conversation but, I was always concerned that we might get questioned about why they were only traveling with one parent in those situations where we did that.
FYI - Internationally, you're considered an Adult at 16 y/o if you do that when your kids are a little older, it won't matter.
Now, as a frequent traveler, one thing that you will want to plan for is - flight delays, missed connections, etc.
So, it would be ideal if you are all on the same itinerary. In other words, you buy the tickets for everybody and have the other parents pay you back. Because, if you have everybody buy their tickets individually and try to get on the same flights, it might be be more difficult to get rebooked if there is a flight cancellation.
I've even had situations where my wife and I were on the same flights but were on separate tickets (mine was paid by work, her's was paid by me), so, it was difficult to get us seated together, or in one case re-booked after a flight cancellation. If they have to re-route you, you'll all want to get re-routed together.