Experience with Emergency AP
If you need an emergency AP, you need a letter/fax from the Hospital where your father is scheduled for emergency. The emergency letter should mention the diagnosis, the surgery details and need for your presence. Ideally, it would be helpful to know the tentative date of surgery and then go about 2/3 weeks prior to intended travel date. If you go much in advance, they will say you still have lot of time and your AP under regular process might get approved by then. I know we need to book the air tickets in advance but this is the way it is. Also, its better to take an Infopass appt but Emergency AP is the only case where USCIS entertain a visit without the Infopass appt. Carry all your docs including the original receipt and copy of docs. submitted during the regular AP process (usually lawyer will have these papers).
Hope this helps and your father gets well soon !
Cheers