Agree with Larry. It sounds like you just want to add a new hose to the end of the current catastrophe that is on your grill. Don't do it, replace it.
First of all, you are right about wanting to change out that current hose. In fact, unless it is just hidden, I don't even think that hose has a regulator on it.
Now, to fix the problem. First of all, you are probably best off removing the manifold from the grill so you have some room to work on it. Then, you have a couple choices for removing that hose. First, you can remove the hose from that little brass angle bracket. To do so you can use a skinny open end wrench (I think 7/16"). Or, you can simply grab it with a locking pliers and take it off that way. Don't worry about damaging the hose...that is destined for the trash bin.
Or, secondly, if you want, you can simply remove the brass angle connector and hose directly from the manifold. Then remove the angle connector from the hose so you can re-use it.
Now buy a new hose and regulator assembly:
https://www.amazon.com/exec/obidos/ASIN/B078K8DSXC/tvwb-20
and you will need this adapter:
https://www.amazon.com/exec/obidos/ASIN/B000BPK76G/tvwb-20
Now, using Larry's advice on pipe sealant above, replace the angle adapter in the manifold if you took it out, then add the 1/8" NPT x 3/8" flare adapter to that using larry's advice. Then install the new hose and regulator assembly to the 3/8" flare connector (don't use pipe sealant). Then check for leaks with a spray bottle filled with soapy water. Then fire it up and starting cooking cow meat.