TriMet is good
Since you say you have ridden this route, I'm unclear on just what you are trying to find out, but I'll give you my take:
I live in Hillsdale. The obvious route from PSU to the SWCC is straightforward: Broadway->Terwilliger->Capitol Hwy->Vermont. The hairy portion is the transition from Terwilliger onto Capitol Highway and to the Beaverton-Hillsdale Hwy split. You are riding through the commercial part of Hillsdale, and, to stay on Capitol Hwy you have to ride in the left-hand lane. This section of the highway can be nasty, with lots of curb cuts, drivers turning right and left, and impatient commuters speeding toward Beaverton. I personally would not feel comfortable trailering a child through this. It's scary enough as a single adult rider.
Unfortunately, I don't have a better route to suggest. Everything I conceive of has its own drawbacks--and would be longer. Perhaps TriMet isn't such a bad idea. Sorry.