"Jeg er i færd med at svømme i min onkels svømmebassin" will be marked as correct.
Remember that verbs after "at" are in the infinitive, "svømme", not "svømmer" which is present. That's where you slipped up in your sentence :)
In Danish: "Jeg svømmer i min onkels pool". "er i gang med at" are completely un-necessary and disturbing over-killing words just to stress the present. "svømmebassin" is a correct word in Danish, but most Danes would use the English word "pool".