Using RCM6700, Is it possible to have two programs in memory and run one after another?

The answer is No.  
Instead you can work to combine the programs into a single program that can accomplish both tasks.

The "Remote Program Update" (RPU) feature allows for downloading a new program and booting into it on the next restart, but that's typically used for firmware updates. The RCM6700 boots the most-recently installed and valid firmware(Dynamic C 10.72E).

But, you could investigate the private _buInstallSecondary() API as a way to toggle between two images. You would install "image A" to the board with RFU, and that firmware would use RPU to download and install an "image B". Each of those images could use _buInstallSecondary() to change which firmware runs at boot.

Be sure to define BU_ENABLE_SECONDARY and BU_TEMP_USE_SECONDARY macros if you want to explore that option. It's non-trivial, and less desirable than just combining the functionality of two programs into one.