Well I don't know if this will help or not, but when my firstborn (who was the most like your second born) got to around that age, I would start to read to him at nap time. I read books that were not really for his age level, things like Jungle Book and he would begin to doze off. Sometimes I would have him in the sling just prior to this, so that he started to get sleepy a bit, then lay him down and start reading. It helped him to begin to sleep without nursing. It's hard when your toddler has rhythms all over the place like that. I think you might have to begin to introduce rituals, rather than wait for them to emerge, so that she begins to make an association/pair the ritual with sleepy time.
I found the "No Cry Sleep Solution for Toddlers" book helpful at this stage. My DD isn't that all over the place, but she still (at 18 months) rarely naps without being latched on, and I wore her in the Ergo for naps until she got too heavy. Some days she sleeps more (or better or worse) than others. I totally feel your frustration with feeling trapped all day! It's like that at my house too, which is why it looks like a pigsty. Hugs to you!
What was HUGE for us was changing her to a floor bed, and making a big deal out of it ("This is YOUR bed! This is where you sleep!") She took right to it, loves to play on it, and now if I ask if she's ready for her nap, she'll often say Yes and actually walk into her room and crawl on her mattress and ask to nurse. Now, she doesn't always nap well after that, but we're working on it - I try to unlatch her using the Pantley Pull Off (from the "No Cry" books), and I also try a little pre-nap routine, like books and the blackout curtains and her little penguin that plays lullabies.
I agree with PP that you may need to introduce a rhythm. You do that by following her sleepy cues for a while, and maybe keeping a log to see the basic pattern. Once you know the pattern, you can "facilitate" it. Toddlers adore routines.