Yes you have to pay to share the second session. But you shouldn't have to pay for skates again.
It looks like they have changed their sessions to be two hours long. Their website says you have to pay each session, so it looks like your understanding is correct. I don't know if this is a summer thing or if they are making a cash grab, but it's definitely a let down. I'd recommend Skate City Overland Park instead. Their website shows traditional times and prices.
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