I guess I will be the dissenting opinion. I don't think she was nuts at all. If your houses are close together and the baby's room is on that side of the house, a shut window isn't going to help much. Some people are light sleepers and some are not. I don't think everyone can be "trained" to sleep through any kind of noise.
My kids are long past the napping stage but it was very frustrating when things your neighbors do prevent people in your own house from sleeping. I remember the days of a neighbor's dog or home improvement project waking my kids from their naps
and then dealing with grumpy kids because they didn't get enough sleep. It isn't as though babies can wear ear plugs. And I'd hate the idea of using a white noise machine every day 'just in case'.
It isn't as though the lady reported the OP. She simply asked if she could delay the mowing. Which The OP did for 40 minutes

(your babies much have taken short naps!!). I see nothing wrong with a neighbor asking for some consideration. Of course the OP is within her rights to do what she wants. But I think the OP is the rude one here.