At close range, the 35 Rem will work fine on your bears. It still has about the 1000 ft-lbs of energy at 100 yards. Like to have more than that for moose, but they are are relative wimps for their size and can be harvested with less powerful cartridges.
The 35 Whelen definitely has more and can do more. Saw a used Ruger No.1B rebarrelled to the Whelen in a store in Grande Prairie yesterday. They were asking $1200 IIRC.
Singleshot rifles are definitely lighter and shorter for stalking.
I do agree that for a nice stalking rifle, it is hard to beat the Winchester or Marlin lever action in 356 Win, and would be a great compromise and fit your needs quite nicely. Ammo can be harder to find, but is not impossible. But the Marlin in 35 Rem may be a better choice for your daughter.
The Browning BLR in 358 Win is also a great stalking rifle and has the added benefit of the detachable magazine and use of spitzer bullets. There are a couple of choices out there for ammo now too.
Have experience with rifles in all of the above cartridges. Have yet to harvest game with the 356 Win and 35 Rem though. The 35 cal is a fun one!