Jnjburkett - Congratulations on beginning your journey to the Truth. It's good that you are so hungry for truth.. Jehovah is a god that satisfies the Spiritual Hunger of everyone Psalm 107:9 "For he has satisfied the thirsty And filled the hungry with good things."
You ask, a really good question.. I cannot answer it from personal experience, but I'll try and answer it from the scriptures..
We have in Jesus Christ the perfect example, of how we are to walk, and conduct our selves..
Jesus is the same one that said John 18:36 "36 Jesus answered: “My Kingdom is no part of this world. If my Kingdom were part of this world, my attendants would have fought that I should not be handed over to the Jews. But as it is, my Kingdom is not from this source.”
and Matthew 26:52 "52 Then Jesus said to him: “Return your sword to its place, for all those who take up the sword will perish by the sword."
It is clear by Jesus words & actions that he condemned War Fare, and none of his followers should partake in any sort of Wars or have any Political affiliations...
Jesus also said... Mark 12:31 "The second is this, ‘You must love your neighbor as yourself.’ There is no other commandment greater than these.” 32 The scribe said to him: “Teacher, you spoke well, in line with truth, ‘He is One, and there is no other besides him’;
When bible principles seem to contradict themselves.. If you follow the two greatest commandments, all else will fall into place.
In your situation, love should overrule any other principle..
Matthew 6:5-10 "When he entered Ca·per′na·um, an army officer came to him, pleading with him 6 and saying: “Sir, my servant is laid up in the house with paralysis, and he is suffering terribly.” 7 He said to him: “When I get there, I will cure him.” 8 The army officer replied: “Sir, I am not worthy to have you come under my roof, but just say the word and my servant will be healed.9 For I too am a man under authority, having soldiers under me, and I say to this one, ‘Go!’ and he goes, and to another, ‘Come!’ and he comes, and to my slave, ‘Do this!’ and he does it.” 10 When Jesus heard that, he was amazed and said to those following him: “I tell you the truth, with no one in Israel have I found so great a faith."
13 Then Jesus said to the army officer: “Go. Just as you have shown faith, so let it come to pass for you.” And the servant was healed in that hour.
Notice here.. Jesus did not say "First resign from your position, as army officer, and then I will help you".. No Jesus read the Army officers heart, and he judged that the Army Officer had.. Great Faith!
What individuals do without proper understanding of Gods Standards cannot be counted against them.. Take as another example, Paul. He was engaging in Spiritual Warfare, Persecuting & Killing Christians.. Despite this, Jesus saw that he had strong Faith, and Jesus corrected his path and blessed him.
You do not need condemn any of your family members, because of their careers in the military.. You can only show love, and serve. God to the best of your Ability. Love destroys all, and they may be moved by your love, to no longer live by the sword as well.