Who must/will replace my car?

Bought a car from a ford dealership, but the warranty is with a Hyundai dealership. The car is already having issues within just 3 weeks. If I request a replacement; which of the dealerships should/would replace it?
The car is financed.
2015 Sonata - 60,000 mile warranty. Only 34K miles on it. Bought it used at 33.9k miles.

You may get it repaired but no one will replace it.

A warranty is a promise to fix something. You will not get a replacement car.

"Who must/will replace my car?"

Service, no replacement.

"Bought a car from a ford dealership,"

Did you get an extended warranty at that time? You might discuss a possible local "lemon law" with them. But 3 days is the usual limitation there in most cities.

"but the warranty is with a Hyundai dealership."

http://www.autotrader.com/car-tips/buying-a-car-is-the-factory-warranty-transferable-228454
… You get 5 years or 60,000 miles, since you are a 2nd owner. And you'd go to Hyundai for that warranty. And that is I believe only for the power train.

"The car is already having issues within just 3 weeks. If I request a replacement; which of the dealerships should/would replace it?"

None will replace it. Hyundai will service it, within the warranty period.

"The car is financed.
2015 Sonata - 60,000 mile warranty. Only 34K miles on it. Bought it used at 33.9k miles."

Nobody is replacing anything. The manufacturer may repair some of the issues if they are under factory warranty still.

The ford dealer is out of the equation. They just sold you the car.

The warranty will repair the car. No warranty on earth will ever replace the car. Your barking up the wrong tree. Nobody is going to replace that car. Your car is still covered under the original new car warranty. Get it fixed under the existing Hyundai warranty. That's what it's for.