Is it possible to remove Vaseline petroleum jelly from fabric?

I'd call a professional carpet/upholstery place to see what they suggest. You might even have them come out to fix it.

Steam cleaning the chair would remove it.

Maybe Fels-Naptha could help?

If it is an expensive chair will your insurance cover it? My Mom-in-Law had friends over and one of them dropped a cigarette on their very nice living room chair. (That was the days when so many people smoked.) Insurance took care of it. May have been the friend's insurance. Their friend was greatly relieved. Reupholstering costs a fortune. Tell your granddaughter that you never really liked the color of the chair anyway.

I would have used rubbing alcohol at the outset. By ironing it you may have inadvertently "heat set" a stain. Here are a couple links - hopefully they work!

http://www.howtocleanstuff.net/how-to-remove-petroleum-jelly-vaseline-from-fabric/

http://envirotechhomecare.com/stain-removal-tips/stain-removal-techniques-for-vaseline/

Vaseline is greasy. But since it's upholstery and it's been ironed, I would get this "Spot Stuff Natural Oil & Grease Stain Remover Packs" - a powder which sounds amazing. Good luck

Try washing with Lestoil and then detergent. Lestoil takes out most grease stains!

I'd wash the pillow cover in Original Blue Dawn dish soap. I'd sponge diluted Dawn on the arm of your chair, dabbing it from the outside in so it doesn't spread. Rinse well.

Vaseline is a petroleum based product ( think gasoline, oil) as the label says, so anything that cleans an oil based stain should work.

Remember those oil spills in the ocean of a few years ago? Dawn Dish Washing detergent was used to clean the oil off wild life like ducks, so it's a safe product to use.

Dawn dish liquid is a life saver. Give it a hobby pouring straight on and leaving to sit for 30 minutes. Then rub in. Then wash as usual. Be careful if using an HE washer as this will make a lot more suds than laundry detergent.