The power steering could be anything from a bad hose, a bad seal on the pump, or a bad steering rack. The hose repair is relatively inexpensive, the power steering pump moderately expensive and the rank very expensive for the age of the car. It shouldn't be hard for a mechanic to figure this one out.
I would check the car very carefully. If it has lived in Chicago most of its life, it may have a rust problem. You are talking about a 17 year old car here. You don't want to put a lot of money into the car to make it roadworthy for this trip.
The Sundance shouldn't be used to pull a 5' x 8' trailer.
I have found U-Haul equipment to be rather expensive when rented on a one way basis. The daughter of a friend moved from Montana to Indiana with a U-Haul truck and towed an older Subaru behind the truck. I am certain that this move cost more than $3000.
My temptation would be to sell the car and furniture and find another car and used furniture when you get to California.