[Disclaimer: Not a teacher]
What context have you seen "related with" in? I can't even think of an example. *think think*
In the British National Corpus, there are 4488 tokens of "related to" and only 8 for "related with". (Check it out: [DAVIES/BYU] British National Corpus.)
"Related to" can mean
a) to have some connection (relation or reference) to something:
She's related to me. (We have a family connection.)
Smoking and bad diet are related to cancer and heart disease. (There is a relationship between smoking/bad diet and poor health.)
b) to establish a social or sympathetic relationship with a person or thing:
He's unable to relate to his father. (He can't "understand/talk to" his dad. This is a naive translation, but most people seem to understand it better when you say that "relate" here means "talk to". Make sense?)
Looking at the "related with" examples from the Corpus, I find one where there's a confusing comma missing:
PREVENTING NEW INFECTION In Scotland the AIDS problem is largely drug related with HIV spreading rapidly through the communal use of syringes and needles during the mid 1980s.
This is highly ambiguous, and NOT an occurence of "related with", but of "drug-related". Compare:
PREVENTING NEW INFECTION In Scotland the AIDS problem is largely drug-related, with HIV spreading rapidly through the communal use of syringes and needles during the mid 1980s.
The verb "to relate" can also have the meaning "to tell", "to narrate" and thus you could end up with a sentence like:
Earbery had none of his wit or power of reasoning: his numerous works are largely made up of quantities of historical narrative, related with a strong ideological bias. (Meaning that he tells his story with a strong bias. This meaning of "relate" has nothing to do with the "connection/relationship" meaning above.)
Sorry the example is to bad, but I just can't think of any other examples of "related with".
I would suggest that when you're talking about relationships and connection, "related to" is your friend, and "related with" is actually wrong. (If you google the phrase "related with" most examples I see - and there's are millions! - are actually incorrect, I think.)
But we need to ask the teachers for confirmation.
Grammar is your friend. Even the gerund.