I did some work on the broken tile area today. Luckily, I discovered no water damage, no rotten floor, but just lack of support. After JIMBO's post, this makes 4 Holiday Rambler's that I've seen or heard of that has this problem, so the way mine was assembled must be typical.
The sub-floor (chip board), only extended under the cabinet edge by about 1/16th inch. The tile went all the way under the cabinet edge. This corner of the cabinet was supported mostly by the tile with no sub-floor under it. I'm amazed that it lasted 13 years before beginning to crack. The edge of the sub-floor was rounded due to the compression by the tile.
I've placed a picture below that shows how the sub-floor only goes barely under the edge of the cabinet. The fuzzy image is the carpet left in the under-cabinet area, that I have now removed.
I used a small bottle jack with support board to lift the sagging cabinet, and then made a support for the cabinet edge before removing the jack. I'll fix the tile after I've found some matching grout. Fortunately, my coach has a couple of spare tiles stored under the bed.