Is this considered an oath of divorce or not, and is an expiation for an oath (kaffarat yamin) required if the husband allows his wife to go after having sworn to divorce her if she goes?

Divorce should not be used as a means of threat, because a conditional divorce takes effect when the condition is met, according to the majority of scholars. If you intended to absolutely prevent your wife from going to her brother's house, then her going would result in the aforementioned disagreement. But if you intended to prevent her only at a specific time, then there is no harm if she goes at another time, and nothing will befall you on account of that.