dravi - you should be flying AA MIA-ORD-DEL - avoid the mess at LHR. The whole T3-T4 disaster is a serious pain.

Anyway - not what you asked so, "practical experience" - you don't need a DAT (Direct Airside Transit visa) if you're an Indian NATIONAL (passport holder) AND one of the following:

* either you have a valid visa for the US (and some otehr countries, I believe Australia / Canada etc.)
OR * a valid USA I-551 Permanent Resident Card issued on or after 21st April 1998;

IF your wife got her Green Card prior to 21st APR 1998, she MUST get a DAT visa or VISIT VISA. In my opinion, it's really recommended to get a VISIT VISA for the UK. They're pricey - but it's so much safer... that way should there be a misconnect or some issue - and you end up having to overnight, there's no issue of "permission" or spending the night in the airport.

Also, if you go thru UKVISAs - it won't stop you from applying - just warn you that you don't need it.