There's no shortcut around the truth of this itinerary: Dallas to Stockholm business class travel currently requires a connection, since no carrier flies the route nonstop, and the smartest routing depends on which alliance perks you're chasing. American Airlines' Flagship Business, in the reverse-herringbone 787 or 777-300ER cabin, typically connects through Chicago O'Hare or occasionally via a European gateway, while United routes Polaris-cabin passengers through Newark or Chicago with lie-flat seats and Saks Fifth Avenue-designed bedding that actually helps on the transatlantic overnight leg. My preferred routing, though, is SAS through Copenhagen — their A350 and A321LR business class cabins feel distinctly Scandinavian in their restraint, and a same-alliance connection at Kastrup is refreshingly efficient, often under 90 minutes if you've checked no bags.
Having flown this corridor more times than I can count for both work and the annual pilgrimage to Stockholm's archipelago in high summer, I've learned that Copenhagen connections beat Chicago ones for reliability from May through September, when Midwest thunderstorms routinely wreck United and American's evening banks out of ORD. My insider tip: if you're booking SAS, try to land the A350 rather than the older A340 configuration on the transatlantic segment — the seat pitch and direct-aisle access are meaningfully better, and SAS's app will sometimes reveal aircraft swaps up to a week before departure that aren't reflected in third-party booking engines. At DFW, Terminal D's Priority security lane is worth using even with Star Alliance or oneworld status, since the international check-in lines can back up unpredictably during peak summer departures.
Stockholm rewards the early riser — Arlanda's immigration moves fast before 8am, and a business class arrival means you can be walking Gamla Stan's cobblestones before the day-trippers arrive. Given how thin premium cabin inventory can get on this Nordic corridor during festival season, setting up fare alerts across all three carriers is the only reliable way to catch the May-through-September sweet spot before it disappears.