After some convicing, Isida seems willing to let us travel with her - when the wagon's wheel is fixed.
Having all of the wheel pieces would certainly help! See if you can find all of them to assess the damage.
You won't need to look too far - there are three wheel pieces to collect, and they're all close to each other. ?
One is obscured, and will require you to look at something in the area to find it.
The first two are in plain view near the wagon:
One is next to the horse. One is still attached to the cart.
The third is hidden in the brush - right-click on the bank slope to find it, then left-click on the same area to pick it up.
Nuri was able to repair the knife when we had all of its pieces, so she may be able to repair this wheel.
Try 'using' it on her and see what she says.
After that conversation, you'll unlock the ability to repair things - open your inventory and click the blue 'repair' icon, then select the wheel.
All that's left to do now is stick it on the axel and tell Isida about your hard work!
For our hard work, a cosy stay inside of the wagon. Use the key on the door and put your feet up!