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Tires weren't your purchase it seems so you could have issues that aren't correctable with a simple balance or maybe even something that isn't a tire issue. Certainly needs to be considered. Bad tire (construction issue). That needs to be considered for sure. You didn't mention age. There's always the possibility that after considerable miles there's no balance going to correct tires that were run "out of balance" or that weren't true when first mounted. Tires are date coded. How old?

Since you're returning it to the second dealer make notes of weight location and amount using the valve stem as a reference before they start. Mark the tire at the valve stem. If there's an excessive amount of weight used presently have them checked as is BUT before the rebalance ask that the tire be repositioned more appropriately to a better position on the wheel. That's the most frequent step not done by any tire shop and used to be the "first move" by a quality shop. Goodyear used to have a weight maximum and if it exceeded that it was policy that the tire be repositioned and the balance redone or the tire replaced. Wheel problems?

If you asked only that either dealer it's been to that the tires be balanced you likely got what you asked for. If you explained the vibration "at speed" and asked for resolution there needed to be "road tests at speed". Some dealer locations aren't in areas that work well for "road tests" certainly not "at speed". Road test certainly seems to be a requirement here. The comments by "jimmy b." - "Dynomite" seem maybe a little misplaced.

Most dealers now have road force but it's not used for everyday services and balances. Going in maybe it's the responsibility of the owner to either request it or ask what equipment is used. Road force would certainly be the desired because it will certainly find problems with the tire being "true" and will usually indicate construction issues.

Your Honda experience should have maybe been your education!