The last thing her father wants is his daughter running off and marrying some GI.
I say this as a former GI that was stationed at the Hump for 2 years! I was a Korean Linguist (98G) and new all sorts of culture and history and blah blah... it didn't really matter though. I looked like a GI and so I got treated like a GI.
If you ask this dude to marry his daughter its not really going to matter which language you ask in, his head is going to EXPLODE. And for the love of all things sacred do not ask while you are still out in the sandbox!!!!
Get your butt back to Korea first. Then, she needs to find a way to gently start making your presence known to her family. Start having dinner with them and be as earnest, polite, and humble as possible. They need to see you as a person. Right now they will see you as a stereotype... a drinking womanizing fighting GI that breaks korean laws and runs over little girls in HumVees. Its going to take some time, but its doable....
Learning Korean in definitely a good start. I wish you luck, man.
oh- and one other thing. talk to your girl about it... she's knows her family better than anybody.