I e-filed through turbotax on 2 Apr 19. The IRS states that they cannot inform me of the status of our refund of $1597. How do I find out what happened?

if it was accepted, then only the IRS can answer.  TT receives nothing further from IRS.

you can go online to IRS website to see if they have a transcript for your 2018 return.  if not, likely efile was rejected - you should have gotten an email to that effect.  did you check you spam folder?   

https://ttlc.intuit.com/replies/7436304