A high priority for you should be keeping it fun for you two. As you get older you will cherish those times together. Don't leave out safety of course but if you can accommodate some of her preferences and still be safe, that would be best.
Riding against traffic on the road is both illegal and dangerous. And highly discourteous to any biker riding in the correct direction.
Biking faster than walking speed on sidewalks against road traffic flow, as been pointed out by others, is also dangerous IF there are driveways and cross streets.
Biking on the sidewalk with Dad can offer good teaching moments - 'See the driver there waiting to pull out in front of us - she's only looking to her left because she's not expecting bike traffic like us coming from the other direction.
Or, 'we're sharing this sidewalk with pedestrians, dog walkers, joggers - many who not hear or see us coming up behind them. As bikers we have to be extra courteous. Sometimes it may be best to walk our bikes."
Good luck.