I was playing this mission and after I went up to the surface and found the shortcut that leads back down to the area to the right of the door of your base. I found the two brothers there fending off a horde. After doing this, they go right through the door without opening it, and then I go to press the button, but the door won't open and my character won't press the button. I tried going away and coming back and still nothing.
You'll have to reload a previous save. If you don't have one, then you shouldn't be too far anyways, so just restart the level. Metro games have occasional scripting errors, that's the only real way to fix them.
You can only save inside of Kshatriya. Are you saying that when you leave and come back, the door is always broken? Either way, if it's not working, you're going to have to unfortunately restart the level.