So here is a weird one and I am just looking for other people's take on it who may have done this.

My Son as I have previously stated is a British Citizen through me, but also and American Citizen.
On doing some digging today I found out that when he enters and exits the US he must use his US passport, but then must use his UK passport to enter and exit the UK....
(so now I have to get his US passport)

Seems straight forward enough however......

When you book your tickets the airline is going to want passport details.
So.. if you enter your UK one so as to not require a visa for the UK how do you check in with your US passport in order to exit using your US passport?
If you enter your US passport how do you enter the UK on your UK passport avoiding any visa mess?

Do you just switch when you get to where you are going? does this not cause any issues?

OK I have both passports too, I've never been stopped or questioned. What I do is, book tickets using my US passport, show US passport in US for Check in and getting through security. Once on the plane I tuck the US one away and use the UK one to enter UK.
Coming back to US I check in, in the UK airport with my US passport, and enter US on my US passport. If you try to check in using the UK passport they'd want to know about your ESTA for the Visa waiver, so use the US one.
UK is only necessary for entering UK (or rest of Europe)

US passport must be used entering or leaving the US. There is no requirement to use UK passport entering or leaving UK. Due to expense, it is not uncommon for married (or even divorced) women to have one passport in maiden name, the other in husband's surname until passport renewal. Most States expect a person to have only one surname. There is no such requirement in UK law. Members of the Royal family have multiple names.

This is the way the duals in our family do it too.

Just did this last week. Worked fine.