I've recently installed new tires with a street tread pattern tires on our Buddy Bike and it has helped handling and made pedalling easier. The trick is finding a tire with a similiar sidewall height. Our local bike store found a Specialized tire that would go to 80 psi that has worked well.
On the pedalling issue, the pedals with cages have made a world of difference and my son is officially in charge of getting us moving. I think you also might try to raise the seat height for your daughter.
Here is a photo of our Buddy Bike.