INSERT INTO returns ERROR 1452
Please make sure you have the value "4" in "id" column in dorogi.activities_category and also change the query to the following:

INSERT INTO dorogi.activities_article (category_id, created_at, title, promo, content, promo_image_url, coordinates, vk_id, updated_at, hot)
SELECT category_id, created_at, title, promo, content, promo_image_url, coordinates, vk_id, NOW(), False 
FROM dorogirussia.activities_article WHERE category_id=4;


Hope this solves your problem !!