Our DD had the same issues with getting water in her face, so I checked with DW, and she traces the solution back to a water park visit where I basically placed an actively-resisting DD4 on the top of the kiddie water slide and pushed. DD sat up at the bottom, recovered from her shock, then declared, "That was FUN!", and the rest, as they say, is history. She worked her way gradually up to swimming in pretty normal stages after that. And in the meantime, the faces she would make as she tried to turn away from the spray at the bottom of the water slides were pretty amusing.
As it has been said metaphorically on this site, sometimes these kids need a push to get over that hump. Well, sometimes they need a physical push as well.
