Elizabeth (the mum) was pretty selfish
She's already accepted she's dying of some disiese, presumebly cancer, and has come to terms with it, knowing she doesn't have long left. When they come up with the plan of having one person work the bait whilst everone else swims accross, she decides not to go as she can't swim and doesn't want to put anyone elses life in danger.
Yet she does not offer to work the bait, which would be the logical option if she wasn't planning on swimming accross anyway, but instead is perfectly willing to just do nothing, letting Pete work the bait, thereby risking his life as he would be the last one accross.