Is what the questioner did—divorcing his wife for the second time while she was menstruating, then taking her back a month and a half later when she was ritually pure—in accordance with the Sharia?

Divorce during menstruation is a forbidden innovation (bid'ah) but is effective according to the majority of scholars. The husband who divorces his wife during her menses must take her back, then leave her until she becomes pure, then he may divorce her or keep her if he wishes. This return (raj'ah) is obligatory according to the Hanafis and Malikis, and a Sunnah according to the Shafi'is and Hanbalis. Your returning to your wife after divorcing her during her menstruation is correct, and there is no sin upon you if you had forgotten the prohibition of divorcing her during that time.