How to implement unsigned subtraction using 2's complement?
I think I should put a 2-to-1 multiplexer where the select input will be the carry out of the circuit I posted. 


Yes, that's all there is to it. 

You have a multiplexer. One input to the multiplexer is the output of the addition (A+B'). The other input of the multiplexer is the 2's complement of that (A+B')'. (Where we're using ' to indicate the 2's complement operation rather than simple inversion)

That means you're calculating the 2's complement of the addition every time, even though you only need it sometimes. That kind of "wasted effort" is very common in digital logic.