I paid for TT Premier 2018. It was rejected. Do I apply for a refund from TT for the online program and then purchase the desktop version?

No

If you have any changes/corrections at all to make to your 2018 return, you now have to complete it using desktop software, which you must download to a full PC or Mac  (not to a mobile device).Then you need to print, sign and mail it.

https://ttlc.intuit.com/questions/2559403-how-do-i-finish-a-prior-year-return-that-i-started-in-turbotax-online

If you already paid for your online software you can ask customer support for a download of the desktop software.

They are available from 5 a.m. to 5 p.m. Pacific time Monday-Friday.

https://ttlc.intuit.com/questions/1899263-what-is-the-turbotax-phone-number

If you are getting a refund, there is no penalty for filing late.  If you owe tax due, then file and pay the amount due as shown on the Form 1040, but expect a bill later from the IRS for the penalty and interest you will owe.  Only the IRS will calculate this—TurboTax will not calculate it.