If you’re suffering from sticker shock, don’t worry. Bathroom remodeling isn’t all or nothing. You can cut down on bathroom remodel costs by going one step at a time. A bathroom can still benefit from new lighting or ventilation updates followed by a new bathroom vanity or granite countertops. You can always upgrade some features later down the road.
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.