Your interpretation is grammatically possible but would result in "to frolic around while lying down or (while) letting waves hit my knees". However, it's impossible to frolic around while lying down. Here, the two actions of the たり-list are 寝そべる and 跳ね廻る:

砂の上に寝そべってみたり、膝頭を波に打たしてそこいらを跳ね廻ったりするのは愉快であった。

It was enjoyable to lie down on the sand, or to frolic around with waves hitting my knees.

Your interpretation is grammatically possible but would result in "to frolic around while lying down or (while) letting waves hit my knees". However, it's impossible to frolic around while lying down. Here, the two actions of the たり-marked list are 寝そべる and 跳ね廻る. The sentence can be rephrased as follows:

砂の上に寝そべってみたり、膝頭を波に打たしてそこいらを跳ね廻ったりするのは愉快であった。

It was enjoyable to lie down on the sand, or to frolic around with waves hitting my knees.