We found close match at Lowes few years ago, try to take as close as possible a picture, most tile places will let you have a sample, take a range of colors around the pictures colors, then lay them down in several places to get a color contrast, and then pick the closest match.
To replace, get one of those Fein Multimaster type tools with a tile blade, HD, Lowes, Harbor Freight sells them. Cut the grout around the broken tiles, this removes the rigidness of the tile from all the rest. Use a small hammer to break the tile into small pieces, clean up that mess. Then using the tool again, you can also get a blade which will chip/cut up the glue used to hold down old stuff. Get down to surface tile was glued too. Put new tile into space and see how it fits, as some grinding with tile blade will be necessary to make sure space is square and clean so grout lines look even.
Get the type of glue which is waterproof, "thin set" won't be best option in MH, since MH flexes a lot going down road, you want an acrylic type which can flex some, tile people should know. Following directions on glue, apply as stated, put tile down onto it, using a rubber mallet, lightly tap tile down to force air out of glue/tile joint. Leave for 24 hours to dry. Then try to match up grout color, and then put it down, may be able to purchase in caulk type tube, easier to put into tight space with less mess. Good luck, grouting is the hardest part of the job with all the clean up, and clean up, and clean up! Get a grout float, and work hard at this point, but it will look better doing this way. Or you can take to RV cabinet shop and they will do it for money.