§ 402. Children forbidden in public homes. No public welfare official shall send a child to be cared for in a public home, and no commissioner of public welfare and no superintendent of a public home shall receive a child in a public home, except that a child under the age of two years may be cared for with his mother in a public home. Such child shall not remain in the public home after he becomes two years of age. Provided, however, that when so authorized by the department a child may be sent to a general hospital connected with a public home or to a separate institution located in the grounds of a public home used only for special or temporary care of children. Provided, further, that the provisions of this section shall not be deemed to prohibit the placement of a child or minor in a public institution for children, as defined in section three hundred seventy-one of this chapter.