As we all know, trading between settlements is, to say the least, difficult. I'm not quite sure why the wagon stops after one trip and refuses to move, even if I rest it and send it back out. I have the resources, and my other settlement needs them.

Is there something I'm missing?

Which settlement are you targeting the trade command on? Trade wagons will carry out exports for the settlement you target them at, and bring back exports from any trade destination.

For example, say A is exporting Mudbrick to B.

If you tell a trade wagon to trade for A, it will see the exports to B and carry Mudbrick from A to B.

If you tell a trade wagon to trade for B, it won't see any exports and will patiently wait for something to do.

You can also check the Trade Route itself, and make sure that enough of the right items are set to be exported. If the trade route is set to export 5 copper, then trade wagons will only deliver copper until the target settlement has at least 5.

A was my first settlement, and B is going to be my military front. I'm sending the rock-resource(is it limestone?) from A to B. A has about 80, the shipments are in 20's, and the trade wagon has stopped at the admin centre for B and is listed as trading for A. 

Note: This was before 2.1, so it may be fixed. I'll go test it out.

I have encountered a similar issue pre 2.1 - it seemed to be related to path finding when cargo paths were saturated at some point with units - now that friendlies can move through each other (and most likely another system tweak) the issue seems to be non-existent even at high loads.

its still in 2.2