Ah, sorry. Looks as if I misunderstood. Rather dramatically.
Did a li'l more research and found this. Here's a map from 1891
showing (at far left) the relationship between the PW&B, the Reading, and the B&O. It is clear that the Reading's Chester Branch did
connect to the PW&B (i.e, Pennsy), rather than to the B&O as I'd earlier suggested.
Slightly more detail is revealed in the 1898 map
of the same area. Again, the Reading's Chester Branch connects with the PW&B on the west
bank of the Schuylkill, at what would become the PRR.
So, I'll withdraw most of what I said earlier. The only way the Reading's Chester Branch could ever have connected with the rest of the Reading system is indeed your first suggestion...that the RDG was granted trackage rights over the Pennsy via the Junction Railroad to Belmont. Trackage rights for which they must have paid dearly, given that the PRR was not in the charity business, particularly where its competitors were concerned.
As for the B&O, you can see where it is a distinct line crossing to the east side of the Schuylkill River, at a point north of what would become Eastside Yard (an awkward arrangement that requires trains to pass the yard, then reverse into it). B&O trains did use their track along the east bank of the Schuylkill to access the Reading at Park Junction to the north (timetable "east").
And for the Fairmount Park (or Art Museum) Tunnel. It opened December 15th, 1886 (and was enlarged in 1921).