If you are just updating a bathroom, you will probably not need plumbing or electrical work. Since this article is referenced to a small bathroom, the costs here are way too high for labor unless you are in Manhattan. $9k for general labor is insane. A small bathroom should cost you $1-2k labor for reframing, concrete board, tile, toilet, vanity and accessories install. Texture and paint should be another $400-600 tops for a SMALL bathroom.
If someone was to come at us with their own additional contract, we would probably decide that we had given them enough of our time and move on. As Nick mentions below, the contractors reputation is the one on the line. They have every reason to do right by you. The crooks of the world generally don't have a reputation to stand on, and as a customer it is your job to research who you are hiring. If you can't find anything about them, they probably aren't who you want to be dealing with. If they ask for money upfront, they probably aren't running a stable outfit. We never take a penny upfront. We collect when the job is fully complete even when we are working on weeks long projects.
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.
I have a miserably small master bath with a particle board subfloor (house built 1969), so I must guy it. I bought toilet made for small bathrooms, and plan to pull the cabinet sink, replace with pedestal, raise storage like lighted bulkhead, demolish tile, and widen doorway from 28" to 32". I might gain 6" from tile removal alone, plus but another 6" on entrance with cabinet sink removal. Since large expense is in demolition, I could do that. But, install showers is tricky given the drain leveling so I'll hire a pro for that. Question: gutting, updating and repairing master bath is necessary, but to what extent should I go i, terms of resizing, which would entail bumping out wall into adjoining small room, which then adds expense of finishing that where window placement restricts encroachment. It's a nice older brick house that I bought before I realized the made of lapses and oversights by the home inspector (who also is a local top police official in a town with highly subjective law enforcement). I need to fix, list, well and leave. Any thoughts (and prayers much appreciated).