I have implemented the functionality using Push Button. When you turn on one Push button all other will be disabled and when you turn it off all others will be enabled.
Yes, this has nothing to do with a radiobuttons and is completely different functionality. I'll have a look what could be simplified. What is the reason that you need it to act this way?
OK, so apparently you need to force the users to turn off the currently TRUE button before allowing him to turn on a different button. There could be reasons for that, so let's have a look at your code example:
I took the liberty to modify your VI a little bit to show what I mean. Modify as needed.
(Another option would be to turn this entire thing into an Xcontrol.)