As far as I know it's the Speaker of the House that is third in line. I am not aware of any vagueness there, but if there is, and this happens, we gonna have a bad time.
Its pretty straightforward.
Present line of succession[change | change source]
Below is the current line of succession for the President of the United States:
No.
Office
Current officer
1
Vice President
Mike Pence (R)
2
Speaker of the House of Representatives
Nancy Pelosi (D)
3
President Pro Tempore of the Senate
Chuck Grassley (R)
4
Secretary of State
Mike Pompeo (R)
5
Secretary of the Treasury
Steven Mnuchin (R)
6
Secretary of Defense
Mark Esper (R)
7
Attorney General
William P. Barr (R)
8
Secretary of the Interior
David Bernhardt (R)
9
Secretary of Agriculture
Sonny Perdue (R)
10
Secretary of Commerce
Wilbur Ross (R)
11
Secretary of Labor
Eugene Scalia (R)
12
Secretary of Health and Human Services
Alex Azar (R)
13
Secretary of Housing and Urban Development
Ben Carson (R)
14
Secretary of Transportation
Elaine Chao (R)[3]
15
Secretary of Energy
Rick Perry (R)
16
Secretary of Education
Betsy DeVos (R)
17
Secretary of Veterans Affairs
Robert Wilkie (R)
18
Secretary of Homeland Security
Kevin McAleenan (acting)
Note Elaine Chow is disqualified because she is a naturalized citizen. I don't believe an acting cabinet official is in the line of succession. But for practical purposes it will be Pence even though he has some involvement in the Ukraine scandal. If chosen one leaves office, I think there will be such relief it will cause collective amnesia about Pence's role.