If Missouri child support intercepted my tax refund how long does it take to get processed

You have to ask them that.

My children's father said his taxes were approved at the end of April. But I never recieved payment.

You'll need to ask the child support department.

And there is a difference between having the tax return accepted and the tax refund approved, they are 2 different things.

my step daughter dads taxs was interecpted on march 22 2019 just called the child support they say they have no clue why its taken this long but they can hold on to it for 6.5 months before releasing it