Hey there, first, I just want to say try not to put yourself under too much pressure with teaching independent sleep right now - any consistent steps you make will be worth it, but especially with an older LO to look after, you'll probably need to do some naps in sling/pram etc and that's pretty normal at her age
Personally, with DD i just decided to concentrate on getting one nap in the cot each day, using shh pat, and APOPed the rest, as I didn't want to leave DS for too long. If the first nap seems the easiest, then perhaps go with that? If you can get another cot nap in then that's a bonus, but otherwise try not to worry too much, she's still so young and will likely your help much of the time - it's great to know that she can self settle at times, but perhaps at other times she's a little more OT or OS or something, so if you see she's struggling to self settle then go ahead and use as much shh pat as she needs. I personally tried to avoid switching to holding unless she was really upset, as I didn't want to confuse her, but I did use the sling a LOT from the start of naps, and sometimes to try and resettle for another sleep cycle if she short napped. I guess I'm just trying to say go ahead and lay whatever good foundations for sleep you're able, but don't feel bad about using props at this age, whether to spend some time with DS or to help prevent DD from getting really OT - after all, if she gets really OT she'll be less able to learn independent sleep.
Other thoughts - could she be OS? Really hard to avoid with an older sibling around! But do take whatever steps you can to keep things calm before nap time, easier said than done, I realise. Also it's possible she may be getting distracted by noises/sights around her by this age - mine certainly did, so a quiet space with white noise and blackout really helped us. From your description, it sounds like she's fairly content, not screaming, just looking around wide awake and dozing off from time to time but not always for very long? What's her A time?