You can get away with only DMG 2, though both DMGs offer valuable advice and you may get more value from the Rules Compendium (though balanced for Essentials, it contains the most recent advice on most mechanics).
The key point here is that you don't need either DMG to build adventures, especially if you have access to the D&D Insider tools like the Monster Builder and the Compendium and have already run published adventures. Strictly speaking, you can infer the guiding principles of both DMGs from those resources.
It's important to understand that the DMGs are more useful as guides rather than rulebooks. You can get valuable advice on what to do in different circumstances and how to build interesting, comprehensive adventures by reading both books. If you're not sure about how to design a campaign setting, not sure about how to build adventure hooks, not sure how to appeal to different personality types of players, not sure how to set dramatic pacing, not sure how to construct interesting battle environments, and so forth, both books offer good advice.
If you're not sure what to do, I'd recommend starting with DMG 1 instead of 2. It has a lot more basic, core advice and covers broader topics. DMG 2 is more of an update that addresses specific shortcomings of DMG 1, which is good when those shortcomings become apparent in your campaign but might not provide the underlying principles you need to construct your adventures. Ultimately, it's hard to predict which book will help you more without knowing which problems you'll run into more.
You certainly don't need any Monster Manual books if you have the online tools: every monster from those books is in the Monster Builder and every terminology element is in the Compendium's Glossary.