A customer is using our dll which is creating a child process which uses an open source library, which ultimately fails because of a call to LoadLibraryExW(), the last error
The best way is to use loader snaps. Basically you use gflags.exe (which is included with windbg) to enable loader snaps; then, run the process with the debugger attached. Loader snaps will enable the loader to print out dbg messages of the process and it will print the failures.
gflags.exe -i yourcode.exe +sls
windbg yourcode.exe