Re: Hatch Act, politically motivated violation of.
It is time honoured, but not the way Obama is doing it. He recently stated that the GOP has to "answer" for letting Trump be their candidate. Now you may think that's so, but you can't deny that it's a low, personal blow against the opposition candidate. It is in no way positive campaigning.
Name a lame duck GOP President (in the last 100 years) who went personally negative like that during a bitter campaign for his successor. Better yet, let me try.
Lessee, there was Eisenhower. Nah, he'd never disparage a fellow service member like that. Hmmm, there's Nixon, but he never got the chance. Ford? Just a big dumb jock, wouldn't hurt a fly, and anyway he was running himself. Reagan didn't need to, nor Bush 1. Bush 2 did, but I don't recall him attacking Obama all that much, or at all really.
I guess that leaves Hoover and previous. Can't really say personally if they did this stuff or not, but I'd guess you have to go further back to find anything relevant.
So no, Obama is not following a GOP tradition, that much we know. As for the Democrats?
I don't recall even Bill Clinton engaging in this sort of behavior as President. Only Obama. Figures.