Firstly, I'd tweak the 2600 a bit. I'd give it a controller with a directional pad, two primary buttons, a select and start button, and a nice rounded design. Essentially a copy of the late-model NES controller. Also, I'd think of something better to replace those godawful switches on the front.
As to software, I'd look to the arcades and start porting over whatever the kids were playing. This eventually worked for Atari OTL, but not until 1980 when they released Space Invaders. I'd try to get on that wagon as soon as possible. I would treat my developers with respect and give them due credit, and thus hopefully avoid their splintering off to form Activision.
Knowing that the glut of third-party developers was inevitable, however, I would pre-empt it with a strict licensing system similar to the one Nintendo used for the NES. I would do my best to lean on retailers caught selling unlicensed games, AGGRESSIVELY hype the Official Seal of Quality in my advertising, and generally be as ruthless as possible in a crusade against shovelware. Perhaps I would be able to stem the tide of cheap-shit games that eventually crashed the market. If not, then hopefully I would have at least disassociated my company from the tide of shit in the minds of consumers.
I'd better hope to avert or simply avoid the effects of the crash, because around 1982 I'm coming out with my second console. For simplicity's sake, call it the Atari 5200. This system, however, would be much different than the OTL console of the same name. It would be backwards compatible with 2600 games, and would be technologically superior to the Colecovision, even if this meant coming to the market a little later.
Now that I've made a name for myself with the 2600, I would begin moving in on fledgling developers whom I know will eventually become important thanks to my knowledge of the what's to come. I would do my level best to sign these companies to exclusivity deals, ensuring that they would only develop for the 5200. I'd do my best to buy the console rights to as many big arcade hits as possible, and I would be a raving lawsuit-happy douchebag when it came to persecuting clones. If I'm selling my console with Asteroids, you can bet the guy trying to sell an identical game called Meteoroids is gonna get dragged into court.
Around the time my neo-5200 is taking off, a little company called Nintendo will be mulling over an entry into the console market. I will committ every goddamn bit of leverage and corporate muscle at my disposal towards sweet-talking them into becoming the exclusive distributor of MY consoles in Japan, under whatever name they like. I'll also promise to aggressively market their games in America, granting them a share of the profits much more generous than that received by a typical developer.
I'll do whatever it takes, because if my new-and-improved Atari can successfully pull
Nintendo into it's camp, it's game fucking over for everyone else. Market analysts of the era will sit around laughing about how I let that Japanese company fuck me in the ass with the generous deal I put forth to win them over, but I know better.
It's the mid-eighties. Say hello to the Atari 7800. As with the 5200, this "new" 7800 will bear little resemblace to it's misbegotten OTL sibling. It'll be technologically superior, and will boast titles like Super Mario Brothers, Metroid, and Legend of Zelda. Cue the Imperial March. Nintendo boasted a marketshare of over 90% at the peak of the NES era, and I plan to do better. Developers will shit their pants with joy when I toss an exclusivity deal their way,
because everything I touch just "happens" to turn to gold.
If Sega decides to challenge me with the Genesis in the late eighties, well, good luck to them in securing third-party developers worth a damn. I'll gut them and nail their carcass to the wall with... the Atari 9600, the SNES of this new timeline. (Bit of a flub on the numbering, but the Atari 10400 just doesn't sound as cool.)
I'll continue with my strategy for the 90's later.