I replaced the nasty, rotting old beige marine carpet in our 2001 Ebbtide Mystique 2300 last year. At first I tried grinding it off, but because it's fairly soft, it just gummed up the grinding wheel, and heated up due to the friction and become impossible to get off that way. So, I then tried using acetone to remove the old carpet glue - but I switched to MEK because it evaporates more slowly than acetone. Wearing a good respirator and working in the driveway, I dumped some MEK on a 2'x2' section at a time, covered it with some thick plastic tarp, let it sit for about 10 minutes, took off the plastic, and scraped off the softened glue with a paint scraper... the kind you can get for $10 that have the front of the blade curved down. It came up fairly easily, but still with a fair amount of elbow grease and a lot of mess!
There are probably better (and likely MUCH more expensive) glue removers on the market, and you may need one depending on what glue was used to glue down your carpet. I think mine was glued with 3M Super 77, which I have read has been used by boat builders for ages. I used stronger 3M Hi-Strength 90 Contact Adhesive to glue down the new carpet, over two thicknesses of that thin closed-cell padding they use under laminate floors (because I had several leftover rolls of it sitting in the basement). It makes the carpet fell nice under bare feet. Two layers of that made a lot of difference!
I used a LOT of the Hi-Strength 90 (and it's expensive), but the new carpet will probably never come loose - and will hopefully outlast me! The new Sapphire Blue carpet is from Corinthian Marine. I bought it because they have a distribution facility about 90 minutes north of me here in GA - Calhoun IIRC. I got a great deal on a large remnant roll, and bought enough extra to have enough to do the side rails, head area, console partitions. etc as well.
It came out looking great - but frankly if I were to do it again, I'd probably spring for Sea-Dek. That stuff is nice. Really nice. Expensive as heck, but really nice! And it won't hold water like carpet will. Everything will just rinse right off.
I wouldn't do Rhino or anything like that... it's great for pickup truck beds but will likely look like crap on a boat floor. Since it's a spray-on product, it's like a very thick paint, and many imperfections in the boat floor will show right through it. I don't think the look is appropriate for a boat... but it's your boat, not mine.
Good luck!
Ken