There are USB 3.x male to male cables that should work for you. Here's one example. -> https://www.startech.com/Networking-IO/USB-PS2/usb-file-transfer-cable-windows-mac~USB3LINK
I have not used such a cable myself but there are several such cables on the market and it appears that they all use the same chip inside. It sounds like they can be put in a "serial mode" or an "Ethernet mode". Each mode is much like it sounds, a serial mode will look like having two USB to serial adapters back to back, and Ethernet mode will look like two Ethernet adapters back to back. Cables like this are generally preferable to pairing up serial or Ethernet adapters because this is faster, 5 gigabits instead of 100 megabits per second, and is cheaper, because if someone were to track down a couple gigabit Ethernet adapters the cost would be far higher.
Take great care in selecting cables because there are still many USB 2.0 devices like this which will only get you 480 Mbps. Even worse are a number of cables that do not comply with the USB standard and will SHORT OUT THE POWER PINS!
There are passive, and USB 3.x compliant, crossover cables (compliant because they do not connect the power pins) that could work if someone could find drivers. Cables like this -> https://www.datapro.net/products/usb-3-0-super-speed-a-a-debugging-cable.html
Both laptops do not have to be connected by the same means. A Thunderbolt cable between the Mac Mini and one laptop will create a very fast network, up to 20 Gbps with Thunderbolt 2. Cables like this -> https://eshop.macsales.com/shop/Thunderbolt/OWC/Thunderbolt-Cables
Connecting everything by Ethernet is a "safe" choice as setting up a network this way is quite simple, low cost, well documented, etc. All you need is a couple Thunderbolt to Ethernet adapters and a hub, or three Ethernet adapters (one for each computer, plus using the one Ethernet port already in the Mac Mini) and connect the two laptops to the Mini by Ethernet. Thunderbolt to Ethernet adapters like these should do -> https://eshop.macsales.com/item/Apple/MD463LLAU/
Here's what I'd do in this case, Thunderbolt to Thunderbolt from Mini to one laptop and the USB 3.x transfer cable to the other. The Thunderbolt connection should practically set itself up, it's things like this that the port was made for. The USB transfer cable is not something I've tried before but the people that make them say they work. If not then return it and get a gigabit Ethernet adapter instead.
The Thunderbolt port on your MacBook Pro is already faster than USB 3 so the fastest possible connection of an external storage device would be to attach a Thunderbolt drive via the Thunderbolt port.
Note that Thunderbolt is a faster interface than a hard disk can accept or push data so for top speed you will either need a RAID configured for speed or an SSD drive.
Best Answer
The device you're mentioning, the Elgato Thunderbolt 2 Dock, provides USB 3.0 ports. As commented by someone else, Thunderbolt is a PCIe extension and thus is not limited by the USB 2.0 bus of your laptop. As such, it is possible for USB 3.0 to be something that is offered by a dock like what you mention.
USB is a feature offered (typically) by the Intel chipset and tends to be driven these days off of one of the PCIe lines from the CPU. Your computer tends to have a controller that translates the PCIe line to a USB interface (in the CPU's supporting Intel chipset) and would support only the specification that it came with. For example, a MacPro3,1 (2008) uses an Intel chipset that supports USB 2.0 devices.
An easy upgrade for those machines is to install a PCI Express card to gain support for USB 3.0 similar to what you'd do with the Thunderbolt dock, i.e. a USB 3.0 controller that sits on the PCIe bus. Of course, any devices on the PCIe bus needs to be recognized by the operating system and thus requires drivers. However, drivers for some USB controllers (e.g. the FL1100) are supported by macOS / OSX 10.8+ and will just work.
Of course, the USB connector does slightly differ between 3.0 and previous specs; the 3.0 connector has a few extra pins that are key to the higher speeds.