Bare-bottom time going well, and a question

I'm so jazzed, I just have to share.

I've had a hard time being consistent with stepping up DD1's PTing with having an infant around too. We're taking a slow, very casual approach with plenty of practice, but still keeping her in diapers. A few weeks ago, I started putting her in underwear once a day, until she had an accident -- then it was back to diapers the rest of the day. She responded all right to that; I think it mostly helped in terms of recognizing the sensation of needing to go, and the consequences if she went in her pants (i.e. being wet), and she would tell us right away if she had an accident. 

Then she started just in the last few days grabbing herself and saying she was having an accident (peeing) when she had a diaper on. So this afternoon while DD2 is napping, I've just let DD1 run around pantless/diaperless on our main floor and brought her potty down here. She has a hard time getting panties up and down and so we're just going without for now.

She's put herself on the potty several times, peed three times, and had only one very small accident before she got herself on the potty! She'll get up and say, "Need to pee" or "need to poop" and then go to her potty -- so far, she's about 50/50 as to whether she actually has to do anything and we've had no poops. But I feel like this is a huge step forward for us, and something that is very doable for me to continue with at least twice a day while DD2 is napping. 

So here's my question: she does a lot of waddling around with her hands between her legs holding herself. Sometimes it means she needs to go, sometimes it doesn't. Is this probably just because she's not used to having that part of her body be naked/diaperless? She does the same thing when she's in panties. Do other kids do this, too?