Hi there I popped over here as I saw your other thread about the night waking.
I realise you have a night or weekend coming up where DH and DD are out of the house so you want to tackle the NWs but honestly this is not something you can 'get done' in a night. As you have said her day time routine is inconsistent and you are often out for family engagements meaning no two days are the same. When there is such unpredictability LO can't really settle into any day time routine or night time routine. The best advice I can offer is to be fully sympathetic regarding her difficulty to sleep and offer your all for her. I know you must be utterly exhausted from broken sleep but the 'fix' for these NWs is to attend to *all* her sleep needs, that means day time sleep needs consistency.
When my DS was young I had 2 non-movable appointments in the week, as his A times and sleep routine altered with age these appointments ended up being at totally the wrong time for him, but as I said they were unmovable so I had to work around it.
Whilst our routine was non-standard it was almost totally predictable. Yes we had hard times (from 3.5 to 5.5 months I was struggling with 4 or 5 40min naps per day for example) but overall I found ways to offer a consistent routine. It seems to me this is also what you could consider, to find a predictable routine which fits within the 'no 2 days are the same' commitments of the rest of the family. It may involve some compromise but this is what families do isn't it?
For DS I committed to his first nap of the day, this would be 'protected' if you like, and no matter what baby groups or invites I had from other mums, family etc, I just said "Thanks for the invite, this doesn't fit with what we need to do, perhaps another time", I did my best to protect that nap even when making doctor appointments etc, not *always* possible but 99% of the time.
I wonder if you looked at your non-movable appointments across the week you might find a way to offer predictable naps for your LO every day even if the routine ended up looking non-standard?
It's possible to move to (almost) set nap times to keep the day more predictable and to fit in with the family commitments, I worked A times for the first nap of the day (gradually extending as needed) but for nap 2 and 3 (especially 3) it became a set time to fit a 40 min CN in before out appointment and another nap directly afterwards (regardless of A time, because this A time was considerably shorter than the first A of the day but it was coming off the back of a CN not a full nap and also needed to fit in before BT). It also meant for mine learning to fall to sleep within 2 mins of being in the car at his set time, that in itself caused me difficulty as he then wouldn't nap at home in his cot for those naps (habit) but as I say it was about compromise and dedicating certain things for LO to enable LO to fit in with the rest of the family.
Just looking at the times of your EASY, your LO is going up to 5hrs between sleep at times, and yet other times after a long nap you try to put her down at only 1hr 20 A time. Honestly this range of A times would effect any LOs night sleep - it isn't because you are doing something wrong in the middle of the night, quite the opposite, it looks like you are responding well at night, waiting to see if she self settles, going in to shush/pat or reassure when she is calling for attention, this is really all you can do, and keep doing, until such time she has predictable day sleep which will help her relax fully and sleep better at night.