We don't often run two trains at once on Karen's Little Railway. The main line track plan (available at www.karenslittlerailway.co.uk/trackplan.php or at the end of this video) is a figure of eight folded over on itself.
It is easy to have two trains travelling in the same direction as each other around the main line, as shown in the first part of this video. The track layout helps to disguise the fact that the trains are simply 'tail chasing' each other.
Although there is only one passing loop provided, it is possible (with some point switching) to run two trains in opposite directions. The second part of this video attempts to show how this is done. One train (in this case the battery electric 'Minx', hauling 2 wagons) travels anti-clockwise around the original oval route. The other train follows the main line - starting from the passing loop, it starts travelling clockwise around the original oval, branches right onto the balloon loop, then right again onto the ladybird line, before finally re-joining the original oval. With some careful timing the two trains can effectively pass each other in two places per circuit.
I found it difficult to keep the trains moving continuously whilst filming and acting as signalman, but I hope the second part of this video gives an impression of how two trains can be run in opposite directions at the same time on the railway.