I think that in order to successfully dissuade your wife's sister from doing this, you need to present her with an alternative solution.
It sounds like, no matter what, you are going to want her to delay the purchase. First, figure out how long she can safely delay buying a car.
Second, I would see if she is open to other models. You say that she wants a Jeep because she works in construction. Which model is she looking at? Maybe another small SUV, or even a Subaru Forrester/Outback would be acceptable to her.
Once you find out these things, you can model different scenarios for her, for example, showing her the total cost to fully finance a 2014 Jeep Grand Cherokee vs. putting down $X. Or comparing the total cost of owning a Jeep Grand Cherokee vs. a Subaru Forrester. Etc. Try using the Edmunds True Cost of Ownership tool or another similar tool to compare different models.
http://www.edmunds.com/tco.htmlYou're probably not going to stop her from buying an SUV, so focus on incremental wins, like getting her to save $1k towards the car, buying a used model, or a more efficient model.