I agree that the child should vent and express her feelings. The opposite is worse, possibly to the point of being destructive.
The question (from what I can tell) is - the OP is asking if the letter should be sent.
If the mother is scared of sending the letter, the content is likely to be damaging. The mother cannot guarantee that the child will never see the father again - so the question is - can the child agree to send the letter and then face the father?
If not, is it not better to keep the child writing letters but not send the letter?
If the child thinks that sending the letter is still a good idea and the child can "live with" seeing the father after, the letter can be sent.
To a 7 year old, I think it's easier to ask the child if they would give the letter to the father personally. If they won't, then I think it's fair to assume that the child wouldn't want to face the father in the near future.
How the Dad might feel shouldn't be the child's responsibility but the dad might be someone insensitive and make it the child's responsibility. If that's the case, is it not better for the problem to be contained till the child is older and better able to deal with emotive issues.
The girl is involving her mother in the difficult issue. Can a person ask - is the mother avoiding the issue because the mother can't face talking to the father, so the mother pushes the responsibility onto the child? I am not having a go at the OP, I am presenting a possible argument that the mother might face.