Yeah, when you count anything in Japanese, you must use a counter word. 人 is the counter word for 子 (or indeed, any sort of people). The formation is [number][counter]の[noun being counted], or [noun being counted]を[number][counter][verb] (as in ビールを二本飲みました = I drank two bottles of beer).

In the second sentence, 人 is still functioning as a counter word – it’s just that 七人の人 is a little bit redundant – you only need to explicitly state the noun when it’s more than just generic people.

Please note, though, that the reading for 二人 is ふたり. It, along with 一人 (ひとり), is a weird freaky exception – for 3 and up it’s on’yomi+にん (except 四人, which is よにん because しにん sounds like 死人 which means “corpse”).