Most economists would say that an increase in the minimum wage will not help to decrease child poverty. There are two main reasons for this.
First, they would say that most poor children are not the children of people making minimum wage. People earning minimum wage tend to be very young, not heads of family who are trying to support others.
Second and more importantly, economists would argue that an increase in the minimum wage will lead to higher unemployment among people who make minimum wage. A minimum wage is a price floor. Price floors always lead to surpluses of the good or service in question. When minimum wage is increased, there comes to be a surplus of labor. There is less demand for that labor at the higher price because firms cannot afford to pay the workers the higher minimum wage. This leads to more unemployment and does not help to reduce child poverty.
with the poverty rate going up, yes