Federalista

Most of the time I think about federalism in terms of the relations between the national and state governments (vertical).  Every once in a while it occurs to me that there is also state to state relations that matter (horizontal).  (In fact I think about it every time I go to the state liquor store.  Utah claims the right to bar its residents from purchasing alcoholic beverages elsewhere and bringing the drinks home.)  So does a state in the United States of America have the authority to bar either its citizens or its residents from leaving the state and elsewhere engaging in conduct which is there legal?  Curious little problem about legal authority and political relations.  The illustrative cases are easy to formulate.  May Utah now bar its citizens from purchasing alcohol in other states?  Or bar them from purchasing elsewhere and returning with their otherwise legal goods?  If you think the 19th and 21st Amendments are an issue, then suppose Roe v. Wade is overturned, may Utah then bar its citizens from traveling to somewhere less benighted to obtain an abortion?  And does it make a difference if we frame this in terms of citizens or residents?  (And what does it take to be a citizen of a state?)