If she is travelling through Europe (especially UK), then she would need a In-transit visa for UK, especially when she returns back from India. I would suggest you should check with the respective country's consulate and also with the Airline.
We had to take an In-transit Visa for UK to travel to India while on AOS and H1/H4 Visa was not valid and were travelling on AP.
In most of the Airports in US, they do not ask too many questions, you would just have to give your PP and AP and they can scan it and will know all the details and would stamp the original and take a copy of it and give you the original. You might have multiple copies of AP, but do not give all the copies to be stamped, just one AP is enough.