All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
First of all, we (Iftaa` Department) commend your being keen on knowing the ruling of Sharia regarding your mother`s work. We ask Allah to make you more conscious of Him and more keen on all that is lawful.
As for her leaving work early and heading home, this depends on the regulations of the Ministry of Education and the system in place. If her doing so is incompatible with the latter and subjects her to accountability or punishment, then it isn`t permissible for her to do what she has been doing. Rather, it is forbidden for her to be negligent and fail to perform the duties entrusted to her. The evidence on this is that Allah the Almighty Says {What means}: "O ye that believe! betray not the trust of God and the Apostle, nor misappropriate knowingly things entrusted to you." {Al-Anfaal, 27}. In case of her being negligent, her salary is a mixture of lawful and unlawful money. The lawful embodies the effort that she had actually made working while the unlawful represents her negligence and failure to do her job.
However, if the regulations of the Ministry of Education allow the above, then there is no sin on your mother Insha`Allah. And Allah The Almighty Knows Best.