The toilet leak during the flush is normally because of the damaged seal in the vacuum breaker. The damaged seal is unable to hold the water and cause a leak. You need to buy the seal and replace it for some RV. Check with the manufacturer to know about it. The initial seal leaking can be prevented with vaseline and rubber gloves. I have seen a product in the market called
plumber grease as a substitute for the vaseline. Keeping the seal moist can be a preventive measure to avoid such leaks. The leaks can also occur from the crack after the winterization. I think porcelain is more prone to cracks. Check the valve and flapper too.
If you haven't found any damage in those parts, better get
assistance from any professional plumbers. I'm afraid to do too many experiments alone. Anxious might it cause any further harm.