You will want to separate the path into smaller components such that you will have the ability to directly affect the line component of your existing path.
Something like this will do ->

You can then have an Expression that links the line to both elliptical paths. It’s also required that you use non-parametric shape paths as they behave in an expected manner with Trim Paths – I am assuming that you would like to draw a stroke along the path without any visual breaks during the drawing process.
For the required Expression for the line path, please post the image I’ve provided along with both of yours in the
COW’s AE Expression Forum.
HTH
RoRK
Intensive mocha & AE Training in Singapore and Other Dangerous Locations
Imagineer Systems (mocha) Certified Instructor
& Adobe After Effects CS6 ACE/ACI