27 months, waking 2x a night

My daughter is waking up at least two times a night every night lately. She was always a great sleeper, but now we can’t get through a night. The only major change is that we started potty training about a month ago (seems to be going well)…

The lack of sleep is messing with us. She wakes up and calls for “mama” and wants us to sing songs for hours. Of course, we do for a few minutes, but eventually we need to sleep. When she was younger we did the taking Cara babies method, but, she’s older now and letting her cry it out feels so cruel. It’s hard to balance wanting to her to feel securely attached against wanting to be rested parents who can be present with her during the day. Any advice? What’s a developmentally appropriate way to help teach a 2 year old to sleep independently?