I am R-1 Visa holder which classifies me as Non-Resident Alien but I passed the substantial presence test mentioned on IRS website! Should I use 1040 U.S individual Forms or 1040 NR forms? Can I also add my wife and dependents who are living in USA with me?

Since the R-1 visa is considered to be a work visa, you are filing as a resident alien.

Hence, you can file jointly with your wife and claim your children as dependents. Do your wife and children need ITINs?

If you need professional help to file this return (and apply if ITINs, if necessary), please email me at the email address in my profile.

So in that case, I use 1040 forms instead of 1040 NR

Yes, that is correct!