As you might imagine, I once had to sue a contractor. He demanded payments up front during different stages of work replacing a roof and front porch on my house. When he wanted to cheap out and use inferior materials, i insisted he do the job to specifications I had provided to him in writing beforehand. He walked away from the job, half completed, and I had to hire someone else to finish it. I recovered most, but not all, of the money he had stolen.
It's so competitive out there. I am a Long Island contractor and I be realized lately that clients give you an impression when you give them there costs that you are doing something wrong. I've been in this Busines about 20 years and that avg cost is right there. Also homeowners should also realize if us contractors are using subs for our plumbing and electrical our costs are hire than the guy doing all the work himself. I only used licensed contractors for all my remodeling work.
Between the two options, pick up one tile design that suits your necessity and budget. Remember to put forward safety for your children in this point. In case your budget is limited, you can partially change the tile. Determine which part of the bathroom that needs new, safer tiles. This will definitely save more money compared to overall tile changing.