Why not take out the carpet and replace with hardwood or laminate? I'm not sure about your family situation, but being a beach house, wouldn't there be sand involved? And if there are children the possibility of bringing that sand to the carpeted areas could be high thereby making it a pain to keep clean.

Just my two cents.

You don't say if you house is on or near the beach, but if it is, carpet is a nightmare. What I have learned in my beach house is to avoid wood and carpet. I replaced my downstairs carpet with wood shortly after I moved in because it got musty (from the moisture) and no amount of vacuuming could bring up all the sand that got ground deep into it. Wood was problematic too with moisture and sand, so after a few years it was looking dull, scratched and pitted from the moisture. I sanded and refinished it, but within a year it started looking bad again, so eventually I gave up and now, downstairs I have wood look ceramic tile (which I love) and an area rug around the couch. I may repeat the tile upstairs, but I am seriously considering Luxury Vinyl Tile (which is an amazing water resistant product that looks great - not like the vinyl of my youth). The great thing about LVT it doesn't require as much labor or prep to install as porcelain tile so the cost is considerably less. You still need to sweep the sand everyday, but the stuff is bulletproof against the sand and moisture.

Carpet in a beach house is a very bad idea.

If you must do carpet, use either commercial or indoor/outdoor.