So, I never had any problem getting Gracie to show up for fashion checks in my town, but my boyfriend has had TIY forever and has never seen her. He has started buying all the the furniture every day, and still nothing.
He doesn't have a very extensive clothing catalog, though. Do you need to have a certain amount of clothing cataloged or anything like that?
You have to spend at least 70,000 bells before she shows up, after that it's random. (There may or may not be a time period before she appears for the first time, I'm not sure.)
I spent around 100,000 bells just to be safe, and then I found something on a website that said how you should probably have outfits prepared for the checks. I realized I had no suitable outfits and that if she did come I would fail badly so I went and ordered them from my T.I.Y. and guess who showed up the very next day T_T when like only half my items had been delivered. Luckily the theme was cute and I passed without having to change try ordering a bunch of clothes? Probably just a coincidence but you never know also I cheated and after I passed I TTd a day back and then back to the check day and did that for all 4 checks.
Other than having spent ~70k bells at TIY I don't think there is anything else you can do to trigger the visit.
Everyone else's advice is really good though, prepare outfits if you get a chance ahead of time!
I'm not sure if you TT but once she showed up once in my town, I TT'd back and forth to finish all four checks.
Gracie shows up randomly and she does appear if it is raining, at least she did in my town. It took awhile even though I had spent the required amount of money. She did appear two weeks in a row so I recently unlocked the dept store. I am so fortunate to have used my two extra residents to pass the required fashion checks as my mayor was not able to complete any of them.
try ordering a bunch of clothes? Probably just a coincidence but you never know 
