how much control do musicians have over their music?

Hannity plays the first 45 seconds of a Bruce Hornsby song to begin each hour

They write the songs, and they play the music. They control that. However, they can't control when and where it's played. ISTR that royalties for playing their songs on the radio are controlled by ASCAP, etc.

Most notably I'm thinking of the Reagan campaign using Born In The USA and Bruce getting them to stop.

I would guess it depends on who owns the publishing. If an artist is smart enough to keep theirs then they probably have more control.

they play music by musicians who most of the time would probably disagree with their opinions. of course this my humble opinion.

... sometimes the artist sells the rights to their music and the company can do anything they want to with it (like sell SUV's).
Paul McCartney was surprised when the rights to The Beatles' music was sold to Michael Jackson (CRIME!!), I don't know all the details of that.

Basically, the corporate music companies screw over artists 'cause they can. If you want your music marketed, you gotta give them what they want. The companies usually dictate the content of the music as well, which would explain the shitty state popular music these days (thank Buddha for the internet!!). Also, most artists only get about 16% of record sales.

Rant over.

If the musician sells the rights, it's not their music anymore.

In American intellectual property law, the presumption is that all phono recordings are available for broadcast. Composers license their work to ASCAP or BMI, which organizations are thereby empowered to collect the royalties due on those broadcasts on the composers' behalf, and they're supposed to distribute this money back to the songwriters.

Flaws with this process:

(1) The songwriter gets the compensation, no matter how significant the contribution of the performer. A good example is John Coltrane's many incredible performances of "My Favorite Things." When played on the radio, the royalties go to the heirs and assigns of Rodgers and Hammerstein, not Coltrane's.

(2) Actually, it may not make it to the songwriter either. They pay the publisher, who's supposed to hand over a reasonable share of the money to the songwriter. There are way too many cases where the publisher keeps the money-- especially in the early days of rock, where the record companies told the artists they had to sign over their publishing rights to the companies.

(3) ASCAP in particular does a terrible job of noting the presence of lesser known songwriters. They think they're doing their job if they just read the Billboard charts and monitor the top rated radio stations, and give all the money (that hasn't been eaten up in "administrative expenses") to those artists-- another example of concentration of wealth.

They'll probably pay attention if a high profile show like Hannity's uses music like Hornsby's every day. Probably Hornsby's publishing company (which Hornsby is probably savvy enough to own) has spoken to Hannity's production company and made a side deal.

It seems Dr. Laura was playing Grateful Dead as before her show. You would think that the Dead would not be her cup of tea.

Very anti-conservative

Standing in line marking time--
Waiting for the welfare dime
'cause they can't buy a job
The man in the silk suit hurries by
As he catches the poor old ladies' eyes
Just for fun he says "get a job"

That's just the way it is
Some things will never change
That's just the way it is
But don't you believe them

They say hey little boy you can't go
Where the others go
'cause you don't look like they do
Said hey old man how can you stand
To think that way
Did you really think about it
Before you made the rules
He said, son

That's just the way it is
Some things will never change
That's just the way it is
But don't you believe them

Well they passed a law in '64
To give those who ain't got a little more
But it only goes so far
Because the law another's mind
When all it sees at the hiring time
Is the line on the color bar

That's just the way it is
Some things will never change
That's just the way it is
But don't you believe them

Prince and George Michael both battled to get out of a contract they felt was unfair.

Formed by Aimee Mann and Michael Penn. She got sick of record labels telling her that her music wasn't pop enough and started her own label. Thank goodness she didn't let them change her. She's wonderful.