Benu. We unnecessarily get worried on this issue. The rules and laws are very clear. The meager income or pension we draw in India is looked after because of the Double Taxation treaty. On your Indian Income you pay taxes. You get a credit for this on your Income generated in USA. In USA if your Income Slab is very high then you may have to pay a small amount of Tax after deducting the Tax you have paid in India. I assure you, You and I will not fall in that category.
Go ahead and be a Resident of USA and also an Over Seas Citizen of India. Enjoy the benefits of the two worlds.
On the Sale of property in India you get exemptions on the the Capital Gains Tax paid in India.
Please go through the site http://www.kpmg.com/US/en/IssuesAndInsights/ArticlesPublications/Documents/us-tax-foreign-citizens-2012.pdf more