Wheeling was in Virginia in 1841...
The Restored Government of Virginia was formed after the special state convention in Richmond finally voted for secession in April, 1861 (after rejecting that approach since the convention statered in February). The northwestern counties in the Allegheny Plateau physiographic province rejected the legitimacy of the decision. They claimed the decision by the convention in Richmond was not legal, because the Constitution did not grant states the right to seceded. Since the elected leaders in Richmond had exceeded their authority, the state government had to be re-formed with new leaders.
The northwestern counties voted on October 24, 1861 to form a "Restored" or "Union" Government of Virginia, and Congress seated their Senators and a member of the House of Representatives. The General Assembly (state government) met at the Federal Customs House in Wheeling, Virginia. Francis H. Pierpont served as governor there until West Virginia became a state. At that point, the capital of the Virginia government (restored or whatever) clearly could not be in another state.