This is not the only story which warns against second marriages and problems with any second wife/stepmother. See for example "Inedrel and his kite" (page 74). A common solution, in reality, was that any child goes with its matrilineal€mother's€lineage.
The mats are sleeping mats (janini) and possibly clothing mats (nieded), all hand-woven from the Pandanus leaf. The process is lengthy and requires skill especially for the nieded; thus mats are valuable.
Lijebake appears as a turtle elsewhere, when giving magical powers to Letao and Jemeliwut.