Can the social service remove a child if his mother does not work officially...?

From what you wrote, we can conclude that social services CANNOT remove a child based on the following.

In accordance with the first and third parts of Article 170 of the Family Code of Ukraine, the court may issue a decision to remove the child from the parents or one of them, without depriving them of parental rights, in the following cases:

• the mother, father shirks from fulfilling their responsibilities regarding raising the child and/or ensuring that he/she obtains a full general secondary education;

• mother, father are cruel to the child;

• mother, father are chronic alcoholics or drug addicts;

• mother, father resort to all kinds of exploitation of the child, force him to beg and wander;

• in other cases, if leaving the child with the parents is dangerous for his life, health and moral education.

Evasion of parents from fulfilling their duties takes place when they do not take care of the physical and spiritual development of the child, his education, preparation for independent life, namely:

• do not provide the necessary nutrition, medical care, treatment of the child, which negatively affects its physical development as a component of education;

• do not communicate with the child in the amount necessary for his normal self-awareness;

• do not give the child access to cultural and other spiritual values;

• do not contribute to her assimilation of generally recognized norms of morality;

• do not show interest in her inner world;

• do not create conditions for her to receive an education.