Plumbing – Best way to split an existing drain pipe

I am trying to tie in a new kitchen sink into an existing drain pipe currently servicing a bathroom on the other side of the wall. Here's the conceptual schematic of what I am trying to achieve:

And here's what the situation looks like in reality:

I am trying to figure out if I can avoid dismantling the existing T-Junction going into the bathroom and installing a new one for the kitchen in that 8" length of pipe, right above the existing junction.

Is this possible/good idea? For example, could I cut out most of that pipe and replace it with stuff like this?

https://www.homedepot.ca/en/home/p.1-12-in-abs-sanitary-tee-10bag-hub.1000109027.html

https://www.homedepot.ca/en/home/p.tubular-drain-connector-15125.1000120040.html

That no-hub coupling says that it works for 1-1/2" or 1-1/4" drain pipe. Does this mean that it can take the existing 1-1/4" drain pipe on one end, and the new 1-1/2" ABS pipe on the other?

It seems that I'd need to fit 2 no-hub couplings and one T-Junction in that 8" length of pipe. Is that likely to work, or is the length insufficient?

EDIT: How much pipe do I need to leave in order for a Fernco coupling to grab it reliably?

Any advice would be greatly appreciated.