I've beat the game with the second ending and I still don't actually know what the Grand Mother wanted- or even if she really had any actual agency in the plot. She just kinda hatches out of the cocoon like she's been in there for decades. It seems like she just wanted a proper silk-based child to replace Lace but even in the first ending, that's not what happens.
The lore overall is a lot less clear than Hollow Knight 1. Weavers seemed to have a good society that just kinda degraded as they became more decadent and focused on silk. I guess there was some sort of internal power struggle?