I wonder if a R-Shiny application works well for a production environment or the only option is C++. I make this question taking in account that R and C++ have a widely set of quant libraries that other languages like Java or Python doesn't have.
R makes a fine environment for quantitative research. Same case with Python. For further information on R versus Python for quant finance, see Is R being replaced by Python at quant desks?
As far as entire production-level algorithmic trading systems go, no. For execution R is generally not used but rather the alpha model in R is integrated into an execution model.
It depends on the frequency of the strategy, however. Online models are ones that are updated in real time, this is more common on lower frequency levels of trading (you cannot have an online model for HFT as it is too latency constrained). In this case, sure you could have an execution program in R however that only increases the complexity of the system because it will involve writing some wrapper in R to communicate with an exchange API since most exchanges (as far as I know) aren’t as R-friendly with respect to execution.
The impracticality of using R (and Python) for everything increases as a function of trade frequency. For higher frequency algorithms developed in R, coefficients from the alpha model developed in R are injected and taken as arguments into an execution program in C++.
There is no need to stick with one language for everything.