Grout is not the name of the material used to set tile. Grout is the admixture used between tiles to fill joints. If you're using grout to set tile, you are using the wrong material.
Thinset or mastic is the material used to set tiles. It comes in different formulas and different types, i.e. powder to mix or premixed. I have good results with polymer modified thinset although mastic may be a better choice for a novice. Unsanded grout is used for small joints between tiles compared to sanded grouts used for floors. Again, it comes in different formulas and types. I have little worries about conventional polymer modified grout cracking or chipping out of joints. Once the tiles are set, there is going to be no movement between tiles. Wherever a moving structure abuts a tile installation, a crack can develop. This is usually handled by covering that joint with a caulk. Silicone seems to be the caulk of choice for this.
There is a vendor out there that hawks a flexible thinset and grout product for RV's. His website comes up towards the top in internet searches. Don't be misled by his hyperbole. Conventional tile installation products work well, especially for installing small expanses like backsplashes.