My H-1B and wife’s H-4 are expiring on June 3. My employer (public schools) will have my H-1B extension filed before the date. I also requested premium processing. However, they said they will not allow me to include my wife’s H-4 application in my H-1B packet; I need to file it separately. Although I asked them to file my H-1B ASAP, I’m not sure when or whether I could get a copy of a USCIS receipt and other necessary info. soon enough that I can file my wife's H-4 extension application before the expiration date.
1. Is it okay as long as the date of the envelope of the packet is earlier than June 3 such as June 2?
2. What if I couldn’t get a copy of my H-1B receipt from USCIS before the expiration date? What else I could do for filing my wife H-4?

We are all in the U.S. now.