Upgrade current bike, or go new ebike
I was in a similar situation to the OP (my kids are now 4.5 and 2, both ride on Mac Ride seats, my p bike is an “ancient” gen1 Bronson).
I’ve made the time argument to myself, in favor of getting an ebike, mostly because in Oakridge it’s like 3500 foot (+/- 500 depending on the trail) climb or nothing at all, since barely any trails there have a way to get on mid-mountain, at least not one that is also a sensible FS road approach. And electric motoring up the shuttle road would presumably still be a better workout than riding in a shuttle van …
But then the drive to Oakridge and back (or Alsea Falls, or Carpenter Bypass, the three places around here where motorized access is legal) is the other very large non-compressible time suck, as is the extra garage fiddle fuckery of owning more fancy and complicated things. So I see the pro running argument very clearly! (But my knees won’t allow it)
Anyways I gave up on the EEB and do a lot more riding of a local trail system 15 mins away that has only 3 miles of descending trails, often I’m only getting 2 miles of descent then heading to preschool to pick up the kids.
The postscript to this is that my wife recently demoed a Transition Relay, absolutely loved it, and also said it would be really dumb to buy only one since we wouldn’t be able to ride together, and most certainly we don’t have the extra cash to buy two, so yeah, that whole idea is dead in the water. Also I need that money for a used electric car so that I’m no longer doing preschool drops and grocery runs in a 3/4 ton crew cab truck, which is super dumb.