I don't have good answers for you, but I've had all of those problems. Especially once my caravan is out, it's always a struggle to get them to come home.
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Yeah, I love love love this game, but it's got a lot of little bugs/quirks/strange UI I'm still getting used to.
I haven't had problems with caravan animals for quite a while. I hitch my horses on temporary maps to keep them simultaneously near the loot and out of lines of fire, but it shouldn't be necessary if you're only in a place for a short time. The last time I did one of those quests where you hack a holy relic/computer, I didn't bother hitching. As soon as I'd finished the hack, I had my pawns flee the map on foot and my horses followed automatically (ignored by the natives).
When you do use a hitch though, does it prevent you from leaving or is that just me? But yeah, I'll try not hitching them next time. I can see something like the reason they don't unhitch is because they're treated differently than pen animals when "caravaned" off colony and that also prevents them from randomly wandering off.
Asking that way.... Maybe it's been years since I've tried. Thinking back, other than the example I gave, I've only left by entering a shuttle or using the Reform Caravan button. That pops up the inventory screen and I'm pretty sure it includes all your animals and colonists by default. After that, you're instantly traveling on the world map--no exiting the temp map.
Alright. I figured out what may have happened. Having more experience under my belt I went to another site. I cleared it and the button didn't pop-up. Once the turret was neutralized it popped up. It's possible I was fleeing the first site because I didn't want to engage or I didn't kill something the game viewed as a threat that I didn't (like a turret). Also, I'm pretty sure I didn't destroy it, I think the battery and generators got destroyed in a fire so it powered down.