Welcome to FMC ownership.  No, it shouldn't have a steering problem as that is not normal.  It appears to me that you have two problems.  The first one is the "shop" that is working on it and the second one is the steering itself.

Unless you cure the first problem you will never cure the second problem.  The most unlikely issue is the steering box and it is also the most expensive to correct.  Much more likely the problem is a combination of the tie rod ends, and the bushings in the pitman (bell crank) that is attached to the frame.  Those are the parts that usually wear over time.

I cannot diagose over the internet and can't tell you what is an appropriate amount of dollars to put into a coach.  That is all a personal issue.  Personally, I am in the middle of an upgrade project on my coach that costs much, much more than the numbers you are talking about.

For the front end issues, I would go to the shop and go under the coach with one of their people and, with someone else turning the steering wheel back and forth, have them show me each and every joint or flex point in the system and determine which ones have any motion at all.  Those are the ones that need to be replaced.  Start with the flex (or rag joint) joint in the steering column and work your way all the way out to the wheels.

I would only let them replace the steering gear if they agreed to refund my money if it doesn't fix the problem.  That will tell you how much real confidence that they actually have in their diagnosis.

Others may have additional suggestions.