A regency would be established until the monarch reached maturity. The age of this varied in different countries - for example, Karl XII of Sweden was crowned King at the age of 15 in April 1697 upon the death of his father, but was declared mature and fit to rule only eight months later in December 1697.

Louis XIV had his mother Anne as his regent, and she appointed Cardinal Mazarin to handle most of the state's affairs until the King was declared to have reached majority at the age of 16 in 1654.

So no, people would not have to obey the child, they had to obey the regent.

A regent could be appointed by the will of the previous monarch, by a privy council or the parliament.