The Secret of Dragonhome (1998) by John Peel?
Melayne and her young brother Sarrow are Talents, hunted by the King's relentless Seekers. If their Talent is discovered, they will be sent to their death. So they must hide...or die.
Melayne and Sarrow find refuge at Dragonhome, the mysterious estate of the shadowy Lord Sander. Lord Sander also has something to hide--a dark and fantastical secret that haunts his every move. In order to save herself and her brother, Melayne must confront forces much stronger than her talent--tempests of magic, desire, and betrayal. If Melayne is not careful, her truth will be revealed.
Melayne must unlock the secrets of Dragonhome. As danger approaches, it will be her only hope.
This review mentions Melayne talking to animals and the brother having a Persuasion talent:
Melayne has the "Talent" of communication, which allows her to speak with anything that is alive (this does not include trees). Sarrow, Melayne's younger brother, has the Talent of Persuasion, you don't find this out till very late near the end of the book. Sarrow's Talent allows him to persuade any human or Talent very easily into doing what he wants, this works better on "normals" (normal human beings without Talents) better than it works on Talents.
The same review also mentions the Seekers, Talents with the ability to find other Talents and send them to war:
They are seen by a Seeker (a Talent who can detect other Talents by the way their brains are) and are braught to the King's House, a place where they prepare Talents for a war completely made to kill all Talents.
Found with the Google query
book talk to animals persuasion war brother sister which returned the Goodreads page.