If the wheelbarrow is already in the character BP, then just connect them with a physics constraint, set the angular and twist limits “to taste,” and maybe add a leaning transform to the wheelbarrow when the character turns. You may need to restrict the character’s sideways movement to prevent full 45+ degree turns, however.
Conversely, you could allow the player to instead control the wheelbarrow, pulling the character behind it with the same physics constraint relationship mentioned above. You would just need to handle any transitions between lone character and wheelbarrow plus character–hide/unhide meshes or spawn/destroy actors. In this scenario, the character is lame, merely moving in-place according to its ABP, while the wheelbarrow provides the actual translation.
In either case, using IK would allow you to keep the character’s hands attached to the wheelbarrow’s handles.
Lastly, the objects in the wheelbarrow would take care of themselves, using standard physics.
Take a look at the UE vehicle template for “car” movement and a youtube physics constraint tutorial for ideas/guidance. The UE free content examples also cover a bit of each subject.