It definitely looks like a watermilfoil to me....Rhode Island is home to Eurasian watermilfoil and Variable watermilfoil (
Rhode Island aquatic invasives website)
Another close-looking plant is Bladderwort, but the leaf structures are different. Also, Bladderwort is a rootless plant, and in your first set of pictures, in the middle picture, you can see a root coming off the plant section in the lower middle of the image.
If you 100% ID it as a watermilfoil (Eurasian, variable or native), the cheapest treatment is liquid 2,4-D (DMA-4 is aquatic labeled). Treat at about 2 ppm and it should be gone in 2-4 weeks depending on temperature.
