Sure you can use Fernco couplings. About the only way to cut in a fitting between two fixed points is with two rubber couplings, the way the san-tee was cut into the fresh air inlet.
Except you effectively have a free end already on the 3" pipe, because it goes to that san-tee with the two rubber couplings. So you can carefully measure and cut out the section of the 3" pipe you need to (either on the vertical for a san-tee, or on the horizontal for a wye), then loosen the rubber couplings to remove the plastic pipe between the cut and the fresh air inlet. That should let you glue in your fitting and then make up the rubber couplings again.
[I'd be inclined to also replace the rubber couplings with shielded above ground couplings, although that may require replacing more plastic (the below grade rubber couplings are around 4" long or more, the above grade shielded couplings are 2-1/8"). Unless I expected to just demo everything out within a year and redo it properly, then I wouldn't worry about the rubber couplings right now.]
Cheers, Wayne