There are so many beautiful things to notice about this bathroom that it's hard to know where to start. The concrete sink? The wallpaper? The sconce lighting? The tarnished mirror on the door, reflected in the main mirror? The barely-there ultra-modern faucets? Whatever you notice first, though, you can't but admit that this space is a masterpiece.
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.