Yes. It came with the pool. I'm using the pump that came with my pool, so it had all the connections and fittings to fit without cutting any holes.Oh yeah, that's so helpful and illustrative! So you're using some sort of double plunger valve as the T junction. Something like this on Amazon? I assume it takes 2 1.25" hoses and converts to a single 1.5" outflow? So is this the reason for not needing to cut 1.5" holes around the twin water outlets (from the pool to the pump)? 2 1.25" holes is enough to feed a single 1.5" hose? And on the other side of the coin, you NEED to cut a hole around the inflow into the pool because it's only one hose and 1.5" is a meaningful increase in size and flow.
I'm not sure if that Amazon fitting is the same, if I remember I can remove the hose from the bottom of my plunger valve tonight and see if it looks the same. My valve does take 2x 1.25" hoses and converts to a single 1.5" hose.
2x 1.25" hoses are enough to feed a single 1.5" hose.
Again I didn't cut any holes in my pool (except for the skimmer), the dual pump inlets were already sized at 1.25" when I got the pool, and there was the pictured supplied dual 1.25" to single 1.5" valve included. I'm not certain your exact fittings, but I saw your post about adapting two 1.25" hoses and figured this might be helpful for you.
It was relatively easy, but I agree you should do one thing at a time. Link in my sig for my install process if you're curious.I don't have that in-wall skimmer but maybe next year ...