First, there's no need to rent a car in Juneau if you're planning to drive into the Yukon. There are car rental agencies in both Haines and Skagway that will supply you with a vehicle, so you don't have to pay for the car on the ferry from Juneau to either place.

The Alaska-owned branches of Avis in both Haines and Skagway will allow you to drop in Anchorage if that's what you're thinking - I was quoted a $300 drop fee in addition to the daily rate. The daily rates charged in Juneau/Skagway etc. are roughly the same as those charged in ANC, i.e. in July, quite high by US standards. Note you'll have to contact those agencies directly to make these arrangements; you can't do so using the global Avis website. Oh and yes, unlimited mileage applies. You should have no trouble hiring a car using your Swedish driving license and passport. The only people that have trouble driving US-registered rental cars into Canada are Canadian residents, due to weird Canadian tax laws.

Now having said that, I just have to offer a personal opinion that renting a car in Haines and/or Skagway and driving (via Whitehorse) to ANC is not the best use of your time and money. While there are certainly scenic portions of the drive from the Yukon to ANC, they are not especially remarkable compared to areas that can be accessed easily out of Anchorage itself, without the need for the 2-3 days' travel between Whitehorse and Anchorage. Driving is expensive, the accommodations available en route are unremarkable to poor, the prices high, and in July you can easily encounter delays caused by road construction/maintenance, or by many other vehicles - RVs, people towing trailers, etc. - on the highways.

Flying from JNU to ANC is quite inexpensive compared to all this, and you could put the same car-hire dollars and accommodation dollars to a better use (IMO) than you would visiting beautiful downtown Tok (not.) You could still take the ferry from JNU to Skagway, drive over the (stunning) White Pass - or take the train - to Whitehorse, then back to Skagway and back to JNU, then fly out - and get some good scenery and a feel for SE Alaska, but then have more time and resources to spend in southcentral/interior Alaska.