[Vuejs]-VueJS add external site to router history

Wild shot in the dark here but the # in your nextpage query parameter is probably messing with the remote site.

What it will see is

QUERY    => nextpage=http://my_site.com/
FRAGMENT => #/entry

so it will redirect back to http://my_site.com/ because it probably ignores any fragment.

You should encode the value correctly, eg

window.location = 'https://third_party_site.com/?nextpage=' + 
    encodeURIComponent('http://my_site.com/#/entry')

which will produce nextpage=http%3A%2F%2Fmy_site.com%2F%23%2Fentry