That is definitely water damage to the flooring; and from the looks of your vinyl stripping, that's the likely cause. I agree, replacing the strip is your best option, and is pretty inexpensive. Unfortunately, the stains will never come out of the flooring. The vinyl flooring also does an excellent job of holding the water under it, and keeping the OSB/Plywood subfloor from drying out. Best thing there is to cut the flooring next to the wall/bench sidewall with a utility knife, then peeling the vinyl back to expose the subfloor. You may have to set something on the vinyl flap to hold it open for several days while the subfloor dries. Hopefully, your floor isn't rotten, and after a few days, you can glue the vinyl back to the subfloor with a little vinyl flooring adhesive (from Home Depot, Lowe's, Menards, etc.). From your pics, it looks like your staining is either inside the dinette benches or under the table between the benches. If that's the case, neither the stains, nor the repair should be that noticeable. I wasn't so lucky on my old trailer. The OSB subfloor was completely toast! I had to cut out about 1/3 of the subfloor with a Dremmal tool, scab in a patch, and replace the vinyl in the entire trailer. Looked real nice when I finished the job, but what a royal PITA! Hope you caught yours in time and it's a simpler fix.
Best of luck!
2013 Eagle 266RKS
2011 Ford F-150 w/3.5L Ecoboost & H.D. Tow Package