Governors can't send troops to other states unless the Governor of other states requests them. And that can be denied by the Governor.
The Defense Department, or the President can request. But the Governors can deny.
If the President 'federalizes' the Guard, then the Governor does have a say still. He, the President, can't federalilze and use the Guard against another state or for use in another state. Posse Comitatus Act. Even then, Governors still have a say. In 1980 Reagan sought to send the National Guard into Central America. Several Democratic Governors refused.
In 2020 several Democratic Governors refuse Trumps call to send troops, National Guard, to the states where rioting was taking place. And the Governor of Illinois warned Trump that no troops should be sent to his state.
In 2018, Governors of 8 states would refuse or recall Guard troops sent to protect the Border Wall with Mexico.
In other words, I am proud of Governor Abbott of Texas in recalling the Guard. In Hind sight, he never should have sent the Guard. Hopefully, these are lessons learned.
Quantrill