My bike, when new 4 years ago, behaved in just that way and I found it just as annoying as you do. After mush careful measuring and alignment checking with a lengthwise string, I found the dropouts were not symmetrical so that the wheels were tilted in opposite directions. After much hemming and hawing over several weeks, I took a round file to the dropouts and carefully filed the slot, checking constantly until satisfied the wheels were straight. The bike now tracks well and I can ride no hands for a bit. The best thing is the bike now tracks well around corners. I'm not 100% satisfied but the bike is mush improved.