I have coolant leaking from a hose directly under my transmission?

Hey.
I have coolant leaking from a hose directly under my transmission. I'm having trouble even finding what the part is actually called.
It starts at the radiator cap as rubber, runs down turns to metal about 12" down. It runs under the transmission and backs up to a fitting just behind the driver's wheel well.
It is leaking from the metal section and the very bottom of the car. Where it runs flat against the trans casing for about a foot, before it goes back up to the fitting.
Can I replace this with rubber heater core hose? Or do I need the metal line? If so, have you any idea what this is called?

The last picture should be third (where the line bends going back up. The leaking is in the downhill side of this area). And the third picture is the best angle I could get of where the hose runs to.
Forgive me, I'm a carpenter not a mechanic. Lol

Thanks, you for your time.