Just my opinion here, nothing scientific.
1. I did not have this problem with my daughter. When she was 14 months old, I’d say “go to bed” and she’d just walk over to her bed (whether day or night) and sleep. All I’d have to do was tuck her in. When she was 3 (after a series of psychologically wrecking events in the meantime) she did need a bedtime story and a hug, but it was still easy to do. She never cries when she’s with me. And she always listens to me.
2. Overall, if you want to do the “let them cry” thing, yes, that’s the right way to do it. As you saw, it worked for the evening. But perhaps you should take it easy on her, she’s only 18m and she just had to go through that phase. I don’t agree with the “mixed signals”. One nap is when the sun is still up, the other when it’s not. Children may not be able to tell the time at this age, but they’re pretty clear about day and night (even plants can tell that difference). So I’d cut her some slack for now.
3. If you’re willing to make the effort of helping her sleep (whether it’s a lullaby, a rocking chair or a bedtime story), then by all means do so. You can never give a child too much love or attention. I have now regretted not allowing my daughter sleep with me every single night she asked me to. I was doing it mainly for me, I wanted her to be in bed by 10 and then have the rest of the evening for me, be allowed to keep on a light and so on. I also wanted to be able to have my girlfriend over sometimes. I only allowed her to sleep with me on special occasions, if she’d done something and I’d said she could ask for whatever she wanted. And what she always asked for was to sleep in my arms that night. I know that most of your children do not have her problem, and I truly hope that they never miss their parent(s) as much as my daughter misses me, but I now wish I could have given her more love, and the safety she wanted to feel, sleeping in my arms rather than her own bed. Yes, there is a time when children must eventually learn to become more independent. You cannot keep them with you forever. But pushing them away so early is also wrong. Let them take their time, hug them and carry them as much as they need it, and allow them to sleep with you until they feel old enough to ask for it themselves. And if you’re a mother, breastfeed for as long as possible.