Slitherine

how or when can you take control of a vassals army ?

Go to Diplomacy on your Vassal. Click on Foreign Policy, then click on it until it says Full Call Safe.
I hope that this helps.

I have a vassal army in my capital. Not able to give any orders. Diplomacy shows cordial 36. Does this need to be higher ? if so, how do I raise it

You gift them in the main diplo menu, or make a very good trade (for them).
You can also change when you should give your their army in main diplo panel
mouseover the round button and click through.
Careful even though they are only half cost, you still pay half ...