From another answer by @harrymc:
A USB 2.0 port gives 500 mA of power, USB 3.0 gives 900 mA.
It's more complicated than that. A USB 2.0 port on a device that is plugged into a host with mains power is required to provide a minimum of 500 mA of current to comply with the spec. A battery powered USB host is permitted to supply less power, but that's a path we don't need to go down now.
The maximum current from a USB 2.0 or USB 3.x host can be 1.5, 2.1, 2.4, or possibly 3.0 amps depending on the revision of the USB spec it follows. A hub port must be able to supply a minimum of 100 mA to comply with the USB spec. That's to allow for a 4-way hub that has 100 mA per port and have 100 mA for the hub electronics when plugged into a host supplying 500 mA. 100 mA is often more than enough power for mice, keyboards, and powered devices like printers and scanners.
Unless the hub is specifically made to support high power devices it must supply only 100 mA to comply with the spec. Some devices want more power than this, and to get the power it wants it might not be in compliance with the spec. One device that takes more power than it is allowed in the spec could trigger a protection circuit, pull the voltage too low for everything to work, or cause some other undesirable behavior.
Because of the complexity on how USB works it can be difficult to find which device is at fault without considerable experimentation and digging into the device specifications. The Targus dock mentioned does claim to support USB-BC power up to 1.5 amps out of the USB-A ports. That should be more than enough power for a hub to have most typical devices plugged into it. The problem is that unless the hub "speaks" USB-BC the hub can't know it has 1.5 amps available to it. It may assume it has only 100 mA available because it is told that it is plugged into another hub. Plug this hub into a port directly on the host and it sees that it is the first hub in the chain and therefore assumes 500 mA is available and so works normally.
How does one resolve this issue? There's many options. One is to do what you have been doing and plug in the dock and the hub directly into the host computer. Maybe a newer USB 3.x hub will recognize that there's more power available on the dock port and so will allow more power to downstream devices. What I offer is a best guess on why your current setup is not operating as desired.