I can understand you're worried about your reservation but I think you're way over thinking things. AI doesn't show my reservation on the their portal plenty of times even when it's a revenue ticket I've bought directly from them!

You could do a couple of things (and you don't have any basis for making a complaint to US DOT):
1. Ask for a supervisor on the phone with AI and take their help to resolve things. This will of course take a lot of time & patience, but if you get a real supervisor on the phone they're quite competent and can actually help you with your problem.
2. If you're going to be in BOM - going to the city office will be an even better way of resolving your query

Don't assume your problem. If you have a valid e-ticket number for your entire itinerary I can't imagine why you're not good to go - whatever the backend PNR issues that TK/UA/AI may have with each other.