Is the existence of West Virginia legal?

[E_querilous_unum]

Absolutely.  Surprises me that anyone says no.

Providing more than a yes or no answer…

1) Constitution includes a clause about process for adding states
    -   before 1861 there had been several precedents for doing this (see Maine for example)

2) Constitutional process identifies two actors in process: Congress and “Legislatures of the States concerned”
- in 1861 there was no question of to who was Congress
- rebellion did create uncertainty as to who was the Legislature of Virginia
- however  Supreme Court ruling from decades earlier (Luther v Borden) ruled on the question of how Congress could decide between competing entities claiming to be the state government
- and the loyalist legislature had been recognized by Congress in 1861
- and the rebel legislature claimed not to be within the jurisdiction of the US anyway

As such, when loyal Legislature voted in 1862 for the creation of the new state it met the Constitutional process

[E_querilous_unum]

Yes, once it had seceded from the Union, Virginia didn't exist as a legal entity with any borders the Union was obligated to respect or any elected representatives the Union was obligated to recognize, so they were perfectly within their rights to instead recognize a Unionist government in exile as the legislature.  

It went down a little different. It was never considered a foreign country.  Secession was considered a null action; Virginia was still considered a legal entity with borders of the US with representatives to be respected and recognized. The “legislature” in Richmond had declared it was not bound by the US constitution, so had no standing in the eyes of Congress, but a small group of state legislators met in Wheeling (not really in exile as it was still within the state), swore allegiance to the state AND to the US constitution and nominated two gentleman to be seated as US Senators (at the time Senators in Virginia were not elected by popular vote but by the legislature); Congress accepted these two into the Senate thus legitimizing the legislature in Wheeling.