My parents are divorced, and I worded mine like this:

Bride's stepdad and mom
and bride's dad,
along with groom's dad and mom
cordially invite you to join....rest of wording...

maybe you could do:
Bride's dad and mom
along with
Groom's dad's full name (John Smith) and mom (Sandy Smith)
cordially invite you...

Or if they're remarried, do it more like the top example.

Hope that helps!