If I were pregnant and had a toddler, I would NOT want the toddler in the same seat with me as a "lap child."
I've never traveled with a lap child, but I have sat in the same row as one--on a flight from NRT to PDX on Delta in the back middle section about ten years ago.
The child was an infant only a few months old and therefore not likely to get up and run around, but the poor mom really couldn't do much except sit there and stare straight ahead for eight hours. Reading or sleeping was out of the question, and she wouldn't even have been able to eat if the kindly couple next to her hadn't taken turns holding the baby.
I have to wonder: was that full flight absolutely the only one the OP could have taken? Weren't there any others, perhaps a day earlier or later, that had room?