What to do when PhD advisor wants student to work on two disjoint projects?
The most important line in your post seems to be one that you didn't give much weight to: "my stipend comes from [the collaborative project]". From my experience, this is a common situation, where the money for your stipend comes from a project you're not interested in pursuing.

Unfortunately, the only real alternative for you is to write your own grant proposal, which is a significant investment of time for both you and your advisor, and carries the not-so-minor risk that the grant won't be funded, which leaves you exactly where you started, with the added problem that there hasn't been much progress on the existing grant.

The second alternative is to leave the advisor and try to find someone else, but I would recommend against that for two reasons. Firstly, it's hard to find someone else with funding on a project you like. Secondly, the problem you're having now—the funded project is less interesting than the unfunded project—is one you'll likely face again in the future. Your advisor's approach of pursuing both projects is (again, from my experience) a typical way of dealing with this, and it will likely benefit you to have experience with this approach during your PhD years.

I recognize that it means extra work for you, and I don't really have much advice on that front. Try not to think of it as extra work, but rather as extra publications in different research areas. That helps minimize the sting.