Sorry, your edit makes no sense. It's not "full grammatical". I don't understand what you are trying to achieve.
Let's simplify your phrase a bit. Who have a coyote manegement program? The city council.
The city council have a coyote management program in place and they
(the city council) have done extensive outreach.
Extensive outreach is the object of the second phrase. You can observe two elements: extensive (adjective) and outreach (noun). They represent what the city council have done.
According to Cambridge Dictionary
an effort to bring services or information to people where they live
or spend time
covering a large area; having a great range
If we include a bit more of context from the article
Neighbors blame city officials for not alerting the entire community.
The city manager tells Eyewitness News that they have a coyote
management program in place and have done extensive outreach.
It means that the city council has made an effort to inform all citizens in a large area about the coyote problem and the coyote management program developed to solve that problem.
The city council haven't done a program to be extensive. They have done a program to control coyotes and they have done extensive outreach to inform the population about that.