Maybe a good start to make this work would be stop calling it "two-timing"? Maybe use polyamory, two lovers, anything other than an actual synonymous of "cheating", for Christ's sake?
The connotation could be different in japanese, though.
since the first girl is aware and the guy is asking for consent, it shouldn't be called two-timing anymore, bc two-timing means straight--up cheating. But this guy ask for both girls consent.