J.S.
Two year olds are very smart. The sippy cups seem more like they are dictating to you what you will and will not do. If it were my 2.5 year old, I have a strong minded one too, I would throw them out and by ones from Walmart that aren't soft but are harder plastic. If they bite them they are done with them. Kids shouldn't have a sippy cup all day long so carrying it around and biting it is not acceptable. I know it's not easy having to deal with strong minded two year old but allowing them to tell you what will or will not be difficult later on.
Good luck !