The following example code will open the Youtube link in the Youtube app if this one is available, otherwise it will open it in a browser:

public static void watchYoutubeVideo(String id) {
    Intent appIntent = new Intent(Intent.ACTION_VIEW, Uri.parse("vnd.youtube:" + id));
    Intent webIntent = new Intent(Intent.ACTION_VIEW,
    Uri.parse("http://www.youtube.com/watch?v=" + id));
    try {
        startActivity(appIntent);
    } catch (ActivityNotFoundException ex) {
        startActivity(webIntent);
    }
}

EDIT: To answer your second requirement. Each time you call a new Intent with this code. It will open the application or browser for this video and it wont show the previous video loaded.

If you have YouTube installed, the YouTube app should be one of the options you get to open the video. When you see this prompt, checking the "Set this option as default" checkbox will make every YouTube link open with the app (you might have to check the option again when opening from multiple browsers, I've had this happen).

This is for Brave Browser only and the navigation that is shown below might change in the future because who knows ¯\(ツ)/¯.

Try disabling “Video playback in Brave” under Settings > Site settings > Media

PS: Similar settings are available in most popular browsers, messaging apps, etc. All you have to do is fiddle around the settings. And most settings won't break/harm your phone.