But the sequence is irrelevant.

HT is equal to TH, because in this situation we only care whether the two coins are equal to each other or different from each other.

It's the percent chance that matters, so it doesn't matter if you can distinguish them. The cases still exist with equal chance.

To elaborate, the situation as stated in the question is currently Hx, so HH and HT are the only possible results.

You can calculate 50/50 but it's not by ignoring the difference between HT and TH.

The first child is not an influencing factor on the second child. It's either a boy or a girl, 50/50.