Not sure about the approval authority, but the request would be in the form of what ever routing mechanisms your unit has, & the packet should include a (for the Army) a leave form (DA31)- LES & what ever else is required for submitting leave, the MOJ. Once you get your LOR, you have a window up until the date of seperation stated on the LOR (about 90 days). The company CDR is required to give you a separation counseling after receipt of the LOR, so make an appointment with the CDR to exactly that, don't wait for them to tell you a date, because you may need that paperwork to get something's done. Do all correspondence via Outlook so everything is an official statement (it really is, if on GOV email).
If you ask for +30 days of regular leave, the request has to go to the Bn as the company CDR can't approve that, he may deny it & stop it at the Company lvl.
Every Army CDR is required to have an open door policy, so if you feel you are not getting a fair shake, inform your chain of command, starting with your first line, & increase your area of impact by going to the next higher CDR in your chain, have your ducks dress right dress, (all the email traffic etc...) & request the PTDY you want IAW regs.
A note of caution here, don't do the blame game, that is don't go in & bitch about how so & so is out to get you. Explain how what you are requesting is going to benefit you & your family(put this in the MOJ as well), also it would really make a good impression if you gave examples of the good things the Army has done for you (you should be thankful and proud of that anyway). Remember you are asking for something that the CDR is not required to grant (they may have to justify why it was denied, but that is just a creative writing assignment). You have to sell it.
At the end of it all, I always have judged the success of failure as how high large of the area of impact was. I do know of a friend who's wife had written (email on blast) to the POTUS, Joint Chiefs, SecA, SecD, and every CDR in the chain, & the ball that went down hill was majestic. All the CDRs were puckered like a rabbits nose (still didn't get what he was asking for, but what a fail). He did recive a bit a razzing, mostly by battle buddies, cause that shit was wicked.