Upvote:0
Here is the process that has worked for me so far (although not in this specific example). Let's assume you have arrived on passport A and want to get to your destination using passport B.
I haven't run into a case yet where a passport was required at the transit location, but I'd use passport B unless it's not permissible in which case things get complicated
Upvote:1
Many countries do not require you to show a passport in transit.
In general when you arrive in a country by air it's not necessary to use the same passport you used to check in with, but it's probably simpler to do that in case they check the passenger list.
Crucially for your question, when you leave a country it's not generally necessary to use the same passport to check in that you show to immigration officers on exit.
Most importantly, it's no business of any airline, nor of any country other than the UK or Ireland, that both countries allow multiple citizenship. If you're ever in a situation in which you need to show both of your passports, you can do that. For example, this could happen if you're in a country where the airline is required to verify your documents on leaving in addition to their having to verify your documents for the destination, and your visas for the two countries are each in a different one of your passports.
When you check in for your flight from India to Indonesia, you will show the airline your Irish passport because it has your Indonesian visa. You will show your UK passport to the Indian passport officer, though, because you used it to enter India.