I've found a solution but it's not an easy one.
Leave the door alone, go to this quest point https://www.ign.com/wikis/assassins-creed-valhalla/The_Gleewoman, free the bard, give her 33 of silver and make her start to follow you. Then fast travel back to Buckingham (it's ok that after fast travel the bard is not with you) and sneak past the guards to the door of the longhouse. Press 'Open by force' (or how it is in English, I don't know) and wait. After about 10 shoulder bashes my bard appeared and helped me to open this [censored] door.

After i opened the door with bard's help cut scene has started and I was able to defeat the guards and free the prisoner. The glitch is gone now.

@sword_gas
By accident of course

@sword_gas
By accident of course

After i opened the door with bard's help cut scene has started and I was able to defeat the guards and free the prisoner. The glitch is gone now.

I've found a solution but it's not an easy one.
Leave the door alone, go to this quest point https://www.ign.com/wikis/assassins-creed-valhalla/The_Gleewoman, free the bard, give her 33 of silver and make her start to follow you. Then fast travel back to Buckingham (it's ok that after fast travel the bard is not with you) and sneak past the guards to the door of the longhouse. Press 'Open by force' (or how it is in English, I don't know) and wait. After about 10 shoulder bashes my bard appeared and helped me to open this [censored] door.