I guess it's a little late to discuss things with husband for this weekend ... but! It sounds like a major discussion is needed about the effect of husband's hunting trips on the household along with some equally major brainstorming for solutions. If your difficult child reliably acts out on these weekends it does her no good to establish that behavior pattern, and you need some support and some respite.
Do you have any services in place such as home TSS or respite services? If so maybe you and husband could plan the hunting weekends for when you can get respite or higher TSS hours. Is there anyone you could hire as a weekend nanny, to have another adult in the house for adult support and rule enforcement? The cost would have to be included as part of the nondiscretionary cost of a hunting weekend. Maybe having a relative over for the weekend? If nothing else the relative would see your difficult child's behaviors and be of help in further discussions with husband.
I'm assuming husband can't/wouldn't take difficult child with him; if she's extremely oppositional it would be dangerous for her anyway. However, he needs to step up and assume equal parenting responsibility. One way could be trade-off weekends to give you a holiday. However, I gather your difficult child behaves better with husband around, in fact he mainly follows through on the rules? ... and that holiday or no holiday, the weekends with husband gone are too hard to survive? If so, he needs to face that and a) hunt less often (!!!), and b) arrange for help at home during the weekends he does hunt. This is affecting your health and for the good of your marriage as well as your sanity, it needs to be worked out, possibly with a counselor.
It would also be good to talk with a counselor about difficult child's reactions/nonreactions to you, and how you can regain difficult child's respect and cooperation. You need her to respect what you say. I'm not blaming you for her disrespect - just saying she NEEDS to respect you and that's another issue to pursue.
Good luck ... put a movie on for the kids and try to take a relaxing bubble bath, or do whatever relaxes you for a half hour ... and get rid of that headache. {{{hugs}}}