I am not sure you can set properties for controls outside of the scope of a control with a style assigned to it. Even if it is possible, it doesn't seem right to do so.
What you can do in your scenario is to use event triggers and storyboards, defined anywhere they'd be visible to both buttons. Here's an example of how to modify BtnLeft, although I'd prefer to put the storyboards a bit further up the tree to allow for reuse if necessary:
<Button Margin="0,0,0,0" Content="Button" Grid.Row="0" x:Name="BtnLeft" Style="{DynamicResource ButtonStyle1}">
<Button.Resources>
<Storyboard x:Key="OnMouseEnter1">
<DoubleAnimationUsingKeyFrames BeginTime="00:00:00"
Storyboard.TargetName="BtnRight"
Storyboard.TargetProperty="Width">
<SplineDoubleKeyFrame KeyTime="00:00:00.5" Value="75"/>
</DoubleAnimationUsingKeyFrames>
</Storyboard>
<Storyboard x:Key="OnMouseLeave1">
<DoubleAnimationUsingKeyFrames BeginTime="00:00:00"
Storyboard.TargetName="BtnRight"
Storyboard.TargetProperty="Width">
<SplineDoubleKeyFrame KeyTime="00:00:00.5" Value="0"/>
</DoubleAnimationUsingKeyFrames>
</Storyboard>
</Button.Resources>
<Button.Triggers>
<EventTrigger RoutedEvent="Mouse.MouseEnter" SourceName="BtnLeft">
<BeginStoryboard Storyboard="{StaticResource OnMouseEnter1}"/>
</EventTrigger>
<EventTrigger RoutedEvent="Mouse.MouseLeave" SourceName="BtnLeft">
<BeginStoryboard Storyboard="{StaticResource OnMouseLeave1}"/>
</EventTrigger>
</Button.Triggers>
</Button>
Instead of the IsMouseOver property, you can use MouseEnter and MouseLeave events. That should give you the same functionality.
Edit: The SourceName
property can be omitted from the EventTrigger
when that trigger is defined within the scope of the button.