Coolant tank question

So my buddy who has a 2001 SVT Cobra. He had major front end repairs don't and the coolant reservoir tank has not just the one top hose that goes from it to the radiator but also has a second hose which is not hooked up to anything so when his system gets to normal pressure the second hose which is located just below the fill cap starts to spit coolant out. The problem is if he gets on the throttle his system in effect pisses fluid all over the place and then over heats. My question is, would it be safe to put a T-fitting in the normal hose which goes to the radiator and hook up this second hose, or would it be safer or smarter to just get yet another coolant tank? I will upload a picture as soon as I move it from my phone to my compute in hopes of it helping out

The hose by the fill neck is the one that goes to nothing and spits and pisses coolant. I was thinking of possibly getting a brass T-fitting and hooking it into the other small black hose which does in fact go to the top of the radiator on the driver side.

Nick, That's the overflow tube, on most cars that just dumps to the ground so as to when the system builds up to much pressure...ie, that which exceeds cap pressure rating (usually 16-19 psi) then the cap pops off internally and allows excess pressure to be vented through that hose............if fluid level was set properly and radiator and t-stat and water pump are all good, you all may want to perform a block check and test for a blown head gasket.....you said he drove the car home iirc after the wreck overheating it in another post??  if such was the case he may have done damage then to it by overheating it.  if it overheats sitting still and or driving it  and all cooling system components are up to par and no restrictions in the system then it could need head gaskets if it initially was overheated bad.

We had done that yesterday, and we're thinking it is a bad head gasket. Mike you are spot on as always and offer great advice. Now we just need to figure out A) cost of repair B) length of time for repair C) if we want to do the repair.

I'll pm you later tonight, I want to ask a friend who owns one of those, in fact he has a 2001, I want to ask him some questions, I'll get back with you.