Until I spotted you had another child i was just going to say "let her sleep at the breast" or "why don't gou cosleep for naps", but I see that's not possible or feasible with a toddler.
Firstly - have you tried a swaddle? It makes moving a sleeping baby easier because it dulls down external stimulation. In addition it recreates womb conditions, which actively calms baby.
The idea would be that you swaddle (quite tightly around shoulders, but loose around hips and legs) before feeding. Feed baby whilst in the swaddle. Lift to a wind position on your shoulder whilst swaddled. Then put down.
Baby will orobably fall asleep on the breast (that's what they do), then be disturbed slightly as lifted to your shoulder. Then go to sleep on your shoulder, then get disturbed slightly when being put down.
Putting baby down is an art form. Try bending your body without moving baby from position, so you are hovering horizontal over crib/basket with baby still on your shoulder. As you put baby down, put your hand on babys chest to recreate the body contact and keep your face close to baby's so she can still feel/hear your breath.
A dummy helps at this point (once put down after winding) so I would persevere with that. Mine wasn't accepting a dummy at 6 weeks and I was beside myself with an unhapot newborn. Be persistant and determined with it. Mine finally 'got' the dummy at 7 weeks after consistant, daily, all thd time perseverance. Blimey was it worth it for independant sleep.
If the swaddle thing isn't happening in the daytime, I'd still persevere with this method at night, since it helps get baby used to being put down not-asleep in the cot. But in the daytime a bouncy chair may be better instead.
Just be relentless about the bouncy chair. Sit on the sofa, bouncer at your feet and keep bouncing baby relentlessly. It frees up your arms/hands to play with toddler.
Keep going with the dummy though, iymts a game changer.
In addition check your winding technique. What worked for your eldest might not work with your youngest and wind causes pain which stops baby settling. Also check your feeding, seek support if needed. A hungry baby is never going to settle easily.