Tool for straightening a bent metal bar of the gate?
Some woodworking clamps are reversable and can act as spreaders, like this model.  I have another style of the "quick grip" clamps that have a mechanical advantage on the grip mechanism and they are reversible.  They can't apply a ton of force, but for that square tubing, you might not need as much as you think as long as the spreader can get a good grip.

The other thing that comes to mind is a common scissor style jack included with cars for emergency tire changes.  You would need a padding material to not scratch the bars, but they can literally apply a ton of force to spread apart the bars.