Another way to think about it is counting the probability of getting k boys out of 2 children.

  0 boys - 1/4
  1 boy - 1/2
  2 boys - 1/4

There's a half chance of getting exactly one boy, and one way to calculate this is by noticing there are two different ways to get one boy if we take order in account. You are right that the orderings don't matter in this case, so we could also e.g. model this with a binomial distribution. Once you know there are >= 1 boys, the chance you have two is 0.25/(0.25+0.5) = 1/3.