We're looking at getting Specialized Amira for my wife. It comes with an SRAM Apex 10 speed drivetrain. I have a Shimano 105 (5600) drivetrain on my bike.

Would we be able to swap rear wheels between the two bikes? Just curious if this would work.

10 speed cassettes are interchangeable.

To clarify the above answer, yes. SRAM and shimano use the same cog spacing on their cassettes, so they're completely interchangeable.

However, your derailleur might not work if it's a super-wide Apex cassette. You may need a long-cage derailleur.