What is the ruling on burying a mother by placing her on her right side with her face towards the Qiblah and covering her with dirt inside the burial chamber? And is this considered "splitting open"? And is there any sin upon the one who does that, and what is its expiation?

The method of burial was explained previously. What the brother did by digging a shaqq (trench-like grave) is not forbidden, but the lahd (niche-like grave) is better than it, based on the Prophet's (peace be upon him) saying: "The lahd is for us, and the shaqq is for others." The shaqq is to dig in the middle of the grave's ground and place the deceased between two built walls. It is better than the lahd in non-solid ground. It would have been better for the brother not to bury his mother in the lower structure, but since the burial has already occurred, there is no sin upon him.