Soakers are knitted or crocheted. They are thicker & bulkier but ideal for overnight!
Some of them (such as Aristocrats) really won't fit under regular pants. Most WAHM ones are trim enough to be worn under regular clothes. (Except jeans...I've not yet found a brand of jeans that CDs period fit under.)
You can just modify what DC wears...overalls work well as do any generously cut pants (such as Hanna Andersson's Wiggle Pants)
Soaker-shorts or soaker-longies can be worn AS clothing (without regular clothes over top). In winter we generally do longies & a long-sleeved tee or longies & a dress as our main outfits.