For 2019, your "father" will file a joint return, checking the box for "this person died during 2019" in his wife's personal information section. You file based on the conditions as of 12/31/19. However, you would need to print your return and sign both spaces with your name and "personal representative." (You might get away with e-filing but I think it's best not to try.)
There might also be a box to check for "this person died in 2020 before filing" for your father, I can't recall.
For 2020, you would only need to file a tax return (form 1040) for your father if he received income in 2020 while alive (2 days). Income received by either parent after 1/2/20 would go on a form 1041 for estates and trusts, and that would require Turbotax Business, which is a PC only program, not available online or on Mac.
