Scenario: There are two really tall solid objects with a gap in between. The gap is slightly wider than the movement tool. An AT-RT or an AT-ST is facing the gap. Can it move through that gap?

The gap is much smaller than the base of the model but the movement tool fits through it. Also the blocking terrain isn't climbable or anything like that.

A ground vehicle can move over anything that is half or less than the model page 38

also think of the movement tool as a train track and the model is the train it still has to move along the path, alsopage 38 left side

If the terrain is not something the vehicle can legally move over, then no. It would have to stop when its base hits the terrain while moving along the movement tool.

This is important to keep in mind when you position anything with a notched base near a building (current vehicles, and future emplacement troopers). Make sure your facing creates a trajectory that allows you to walk around the corner. Otherwise, plan on using a pivot before getting around the building.

1 hour ago, Rogue Dakotan said:

Scenario: There are two really tall solid objects with a gap in between.

Really tall? So height two?

Then no, the vehicle cant. And if it's a snow speeder it crashes * if it cant avoid contact.

*edit.

All minis are supposed to slide along the movement tool. If their base clips something, they are supposed to stop moving unless they have an ability that lets them continue past it. Many, many times I see people trying to skirt around barricades with troopers at speed 2 and the tool touching the barricade. That's a no go.