Hi there and welcome
You've already received great advice from pps, so I'm just here to say yes I know exactly what you mean, had just those same thoughts, especially with my first! The books can make it all seem too easy and I have to say I got on much better second time around, once I'd adjusted my expectations. I'm sure there are some babies who have a much easier time settling for sleep, but I think many of us who ended up on these forums did so in desperation because ours weren't!
Just bear in mind that your goal right now is teaching her to sleep independently, but that doesn't mean she'll be able to do that all the time just yet. Some LOs may at this age, but many others just need our help with soothing for a few more weeks, then we gradually need to do less and less until eventually they 're able to fall asleep without our help...until teething strikes, or a sleep regression, or it's time for a routine tweak, or... But once they've learned that skill, it's generally easier to get them back on track again after a regression. There's a lot of developmental stuff going on at this age, as well as growth spurts and a need to increase A time, so don't expect perfection. But every time you or your wife is at your DD's side helping to settle her to sleep, without leaving her to cry by herself, you are teaching her that she is safe and secure, that you are with her when she needs you, and helping her to learn how to soothe herself by showing her what it 's like to be soothed, if that makes sense? You might find this an interesting read:
Research on why 'cry it out' and 'controlled crying' is NOT recommended! So this work that you're doing is all valuable, and it sounds like she is starting to get it, actually, if she sometimes goes down happily and it sometimes only takes 20mins, that's great! What you should begin to see is that this happens more and more, but it will take time.
The other thing I wanted to mention is that it sounds like you're both doing a really great job watching her cues and responding to them. However at this age, many of us find that cues start to get less reliable - for example she may just be giving you tired cues because she's used to going to sleep at a particular time after her last nap, but in fact you need to keep her up just a little longer in order to help her to get a longer, more restorative nap. So keep logging her timings and see if you can spot patterns - eg she might take a great first nap if she has an A time of around 1h45, for example, so try and stick with that. Or she might scream her head off if her A time was more than 2h15, so in that case you'd probably try and avoid that and get her to bed earlier, even if she hasn't shown you tired cues - perhaps she'd just got really interested in something else and didn't realise she was tired. Does that make sense?