What does the door sticker say for GVWR? You don't mention your family size, but since you're looking at a bunkhouse, I assume you have kids. This means even more cargo, bikes, etc.
Keep in mind that the trailer you're contemplating weighs as much as the Santa Fe. As others have mentioned, the sail effect of a hard side trailer is significant as well. Your Hyundai would probably pull a 5,000 pound boat very well, but a travel trailer is a different beast. If it was me, I'd be looking at something lighter, maybe without a slide, or a popup.