saltywitchcraft When you've installed the game through Steam, you need to repair through Steam. But it sounds like you've found the "Verify integrity of the game files" option already, which is what a Steam repair is called.
Having said that, this sounds like a couple known bug reports, for example this one:
UI Exception 1009: UI removed, Black Screen and unresponsive game | EA Forums - 12229599
The important question is whether you get a lastUIexception in Documents > Electronic Arts > The Sims 4 when this happens. It would be best to delete any you already have, then trigger the error again and look for a new file. If you find one, open it, copy its text, and paste it into a reply here.