The phrase "looking forward to your understanding" is correct and usable in written English. You can use it whenever you are expressing the sentiment that you would like the person with whom you are communicating to understand your perspective. For example, you might write "I understand that this is an unexpected request, and I am looking forward to your understanding of the situation."
Are you looking forward to your show?
Start looking forward to your big celebration.
Nanjing Normal University is looking forward to your presence.
We look forward to your responses and to understanding more about these disturbing dynamics in future hearings.
I look forward to your submissions.
I'll look forward to your company.
I look forward to your Martin Luther King.
I look forward to your questions.
We sincerely look forward to your rotation!
We look forward to your submissions!
We look forward to your participation.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com