2 separate signature fields in 1 form

It looks like you use regular PDF forms, not the Adobe Acrobat Sign stuff, and that you expect digital signatures, not some wet signature images.

In that case they cannot sign at the same time, they must sign one after the other. They don't need to send the PDF back to you in-between but applying the two signatures  needs to happen in distinct calls of the signing procedure. Also it is their job to make sure that each of them uses their own private key / certificate.

Sign works by sending emails to each signer individually.  You can send the form to be signed simultaneously by both (meaning it doesn't matter the order it is signed) but they each have to clic on the link sent to theit individual emails.