Is it considered a sin to involve brothers in a project if the husband accepts his wife's condition not to involve them, or if there is uncertainty about accepting the condition, knowing that she does not contribute financially?

If you intended to fulfill a promise, but then it became clear to you that the good lies in sharing with your brothers, then there is no blame upon you for breaking the promise due to a valid excuse. However, you would be sinful if you intended not to fulfill it, or if you had no valid excuse. You should also appease your wife, for "the best of you are those who are best to their families."