The car stumbles and falls on its face after slowing down. I think it might be the fuel filter but wanted a second opinion.

It's doubtful this is the fuel filter. If you want to make sure fuel pressure is ok then rent a fuel pressure tester at a parts store. You should be right around 60 psi. If you have a check engine light on scan the car as well. This sounds like it could be a tps issue or even a vacuum leak. If you don't normally work on your own car and need a shop, use this link to find a good one near you. https://repairpal.com/repair-shops Alex