You must remove the surplus had because there is no past-past-perfect. The sentence would be easier to understand if you added a colon and a couple of thats.
Last night I was thinking about my new year's resolution that I had set: to finish the painting for my mother that I had started to draw last summer.
This sentence is complicated, but grammatically correct. A reader would understand that:
- Last night you were thinking about your new year's resolution.
- You made the new year's resolution at some time before thinking about the resolution.
- You started painting the picture before making the new year's resolution.
The reader cannot deduce the third point from the use of the past perfect I had started, because that could also indicate that you started the painting before thinking about your new year's resolution.
The reader can deduce the third point because the new year's resolution is about finishing the painting, which means that you must have started it before making the new year's resolution.