Is this the correct use of the word otherwise?
With these workshops the children and parents take home valuable knowledge about farmers and food that they would not otherwise receive.
I think children have many sources to receive such information.
But OK. Your question was about using 'otherwise'.
Yes, you use 'otherwise' correctly.
You can use 'otherwise' to say smth. like:
Sometimes children's charities answer letters in poor communities, or from children's hospitals, and give them presents
they would not otherwise receive.