Maybe a small peice of vinyl trim to hold it down would work.
Bolers original linoleum floor was cut to fit full floor up walls about 1" no glue. Cupboard frames fastened to walls and floor with brackets using rivets and screws. Frames rest on floor with screws going through the linoleum that floats on plywood below. Problem is how to ever replace it with out removal of cupboards. Not being glued allows for trailer flex. Our trailer the trailer has a very light weight
1/4" thick indoor outdoor rug that has a waterproof film on bottom filling center floor area held down with trim, it is working for now.
Do not know Casita construction though.