Dear Mr Vishnu,
Shifting your son to Chennai would be advisable only in case your son is really interested in joining in the IITs.
He should be able to handle the stress of the preparation for two years staying in a hostl away from home. If you think he can do it, more importantly if that is what your son feels then definitely you can put you son in FIITJEE.
The best centre for FIITJEE in Chennai would be the centre in "Vidya Mandir School" in Kilpauk.
Try to get him an admission in this centre. The facilities would be coherent for the preparation for IIT-JEE or any competitive exam at the national level.
P.S; Sir, on a lighter note, please avoid addressing anyone here as Sir. I suppose we are all very young trying to sort our querries of students aspiring to take up any competitive exam.
Wish your son all the very best.
Ashwin (IIT MadraS).