You shouldn't be parenting his daughter anyway - helping out by babysitting, maybe, while he's out hunting or whatever, but not in a parent role (that means, if SO is there, he takes care of her).

As for the pick-up with BM - DON'T DO IT.  Tell SO to pick up SD and then swing back and get you.  Really - don't poke the bear. 

Honestly I would go. But don't watch SD. You said YOU enjoy hunting. It's a vacation for you, not a nannying gig. Let your SO, or his family care for SD, and you go find yourself a deer, or rabbit, or turkey, or whatever it is you're looking to hunt!!!

However I like the idea where he swings back to get you after getting SD. I personally enjoy poking the bear a little (Think sickly sweet, or saturday I'm going somewhere, the skids, GBM, and Psycho will likely be, and I'm just going to be ridiculously nice to piss them off...) but if she's super awful, then just avoid her, no need for extra drama at the start of your vacation!!!

If It were me I would add disclaimers at each turn:    

if he told you BM doesnt want you around SD, I would say "sense you are more worried about BM's happiness, I better stay home so we dont upset BM, Im not one to sneak around."  

disclaimers:

If you go and family members start talking to you about BM, I would say "Wait, they are not still married are they? because I dont date married men."   

and if they are talking about BM and you are not apart of the conversaiton, i would say "wait, now who are you talking about?" and when they say BM and laugh and reminess about better times in front you you, I would say "it sounds like they were a great couple, why did they get divorced?"  

and if SIL says they still love each other and will get together again if you walk away, I would tell DH "your sister says that you still love each other and will get together if you walk away, so im WALKING so you guys can get back together, Im not one to break up a marriage".       

and I would just keep repeating "Wait are you sure they are divorced, because I do not date married men." until they stop talking about her in front of you and SO.   

and also, when MIL starts some agressive conversations, when DH steps away, I like to say real loud so he can hear me when he left the room "DID YOU HEAR THAT, DH? your mother is saying that you guys used to have great family get togethers with BM, but they dont get to do that anymore with her, what do you think of that? why dont you guys have great famliy get togethers with BM anymore!?" and bring DH into the conversation with mil so I can escape and they can work it out. 

If you haven't met his family, you have no idea how they will treat you. You crept on FB and made some presumptions, but you still have to give them a chance.

Now, this stuff about changing the plan the day before you leave...that's crap. You must break your SO out of that habit. You can do it calmly by just explaining you're nervous about meeting them and the last minute change made you more anxious. Most men, although more easy going than we women, will understand if you're honest and say you just would have liked more time to get used to the idea so you can make your best impression. Trust me, you want to nip this in the bud so you always know what you're getting into regarding the skid, the BM and his family.

More importantly, he needs to stop thinking like a single person and start thinking like a coupled person. He should NEVER agree to any change of plans that affects you without saying, "Let me check with Kbee and get back to you," no matter who the plan is with -- THIS IS STRAIGHT FROM OUR THERAPIST. This is important, especially with SD3 so she sees you as a factor in her own wants and someone who must be considered part of her dad's life. It's also important if your suspicions about his family's tie to BM are true. He must present you as a couple so you are respected and accepted as a part of his life.

If you're nervous about a being there for the skid exchange, tell him that and don't go. BM has already made it clear that she is not cool with you. Why antagonize that? Let him drop you at a McDonald's near BM's house or let him come back to get you at home. If you stir this pot early, it will only make things harder with BM down the pike. While BM may have no right to cause a scene, people will do what their emotions dictate. There's no reason for you to become more of a target and there's no reason to flaunt your relationship in BM's face. It's just unnecessary. Wait until you have a better idea of how these exchanges go and until BM has a nice long time to digest that a new woman is in his life. It may not seem fair that you must do that, but why bring more conflict into the situation?

Do's and don'ts with the family...don't drink alcohol -- that may loosen your tongue or make you misread things in the moment.

No matter how angry you may get over anything, hold your tongue. This may be the start of a long relationship, so don't say anything to burn bridges now. You can duke it out when you're alone, but if the whole clan is there, they will rally around their blood and likely see you as the bad guy if you take your part too much. Expect there may be things said or done that you don't like, but keep it to yourself until you're alone with him and can address it then.

Be attentive to SD, but not too hands on. If she's playing near a hot stove, gently direct her elsewhere. If she's being a brat, act like you are in the cone of silence and don't discipline or respond. That's for her family to deal with not the new woman on the scene who might be read as overstepping.

Otherwise, just be your charming self. If you put your best self forward to them and you're light and engaging, they should like you. If they don't, that will tell you something about your challenge ahead. But if you show them any ugliness, you'll never know if that made them dislike you or if they just won't accept a new woman in his life.