@Piotr Bugalski has recently re-written the firmware for this motor shield, and published it at https://github.com/pbugalski/wemos_motor_shield. From what I can tell, the new firmware is compatible with the old one, minus the hanging and crashing, so it should be perfect for a drop-in replacement.

Here is how you can flash it to your shield:

Solder two wires to the first two legs of the microcontroller, counting from the top, like this:

Be careful to not short them with the legs next to them. This is probably the hardest part.

Next, connect you ST-Link programmer as follows:

SWCLK ↔ first wire

SWDIO ↔ second wire

GND ↔ GND

3V3 ↔ 3V3

T_JRST ↔ RST

Note that, this is with the shiled *not* connected to the D1 Mini.

Now, clone the repository:

$ git clone https://github.com/pbugalski/wemos_motor_shield
$ cd wemos_motor_shield

Make sure you have installed openocd and arm-none-eabi-gcc. Compile the firmware:

$ make
arm-none-eabi-gcc -Wall -g -std=c99 -Os -mlittle-endian -mcpu=cortex-m0 -march=armv6-m -mthumb -ffunction-sections -fdata-sections -Wl,--gc-sections -Wl,-Map=motor_shield.map -Iinc src/startup_stm32.s src/main.c src/user_i2c.c src/tb6612.c -o motor_shield.elf -Tstm32f030.ld
arm-none-eabi-objcopy -O binary motor_shield.elf motor_shield.bin
arm-none-eabi-size motor_shield.elf
   text	   data	    bss	    dec	    hex	filename
   2032	   1084	   1056	   4172	   104c	motor_shield.elf

And flash it onto the shield:

$ make program
openocd -f stm32f0motor.cfg -f stm32f0-openocd.cfg -c "stm_flash motor_shield.bin" -c shutdown
Open On-Chip Debugger 0.9.0 (2015-09-02-10:42)
Licensed under GNU GPL v2
For bug reports, read
	http://openocd.org/doc/doxygen/bugs.html
Info : The selected transport took over low-level target control. The results might differ compared to plain JTAG/SWD
adapter speed: 1000 kHz
adapter_nsrst_delay: 100
none separate
srst_only separate srst_nogate srst_open_drain connect_deassert_srst
Info : Unable to match requested speed 1000 kHz, using 950 kHz
Info : Unable to match requested speed 1000 kHz, using 950 kHz
Info : clock speed 950 kHz
Info : STLINK v2 JTAG v17 API v2 SWIM v4 VID 0x0483 PID 0x3748
Info : using stlink api v2
Info : Target voltage: 3.490340
Info : stm32f0x.cpu: hardware has 4 breakpoints, 2 watchpoints
stm_erase
target state: halted
target halted due to debug-request, current mode: Thread 
xPSR: 0xc1000000 pc: 0xfffffffe msp: 0xfffffffc
auto erase enabled
Info : device id = 0x10006444
Info : flash size = 16kbytes
target state: halted
target halted due to breakpoint, current mode: Thread 
xPSR: 0x61000000 pc: 0x2000003a msp: 0xfffffffc
wrote 4096 bytes from file motor_shield.bin in 0.287988s (13.889 KiB/s)
target state: halted
target halted due to breakpoint, current mode: Thread 
xPSR: 0x61000000 pc: 0x2000002e msp: 0xfffffffc
verified 3116 bytes in 0.057512s (52.910 KiB/s)
shutdown command invoked

Now, disconnect everything. Your board has the new firmware on it. You can test it, and then desolder the two wires -- you won't be needing them anymore.