Hi again,
It sounds like tackling days and nights together might be the way to go, at least that's what I get from your post? Yes PUPD with shh/pat would work well, you may have to adapt the shh pat a little (e.g. just rest a hand on her back) as older LOs sometimes find it annoying, but you'll find the combination that works for her best
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With feeding before sleep I would probably try to offer a feed just slightly earlier than you are doing now, then change her nappy afterwards before trying for a nap. Gradually bring that feed earlier and earlier in her A time until it's at the start rather than the end. You may however find if she feeds less at night she may be more hungry and willing to take a feed in the morning which sets you off on the right track.
At bedtime, I always fed my DD right before sleep in the early months. I then started reading a story to her during the feed, and taking her off just for a few seconds at the end so there was a bit of story before she went into the cot. Over time that became feed, then sit up and cuddle for story, so that when we dropped the BT feed she was used to story then bed.
With night feeds I would suggest you have a very clear plan that you can stick to, as with the best will in the world it is hard resisting the temptation to feed at 3am when you're exhausted. You basically need to have it clear in your mind before you go to her whether this is a 'feed' or 'not feed' waking. I think it would be hard on her to not feed at all overnight given she is used to being fed frequently. So what I would suggest is note what time her bedtime feed is, then work out when 4h later would be. Make a note of that time e.g. BT feed at 7pm, 4h later = 11pm. And then if she wakes at night check the time. If it is after 11pm, go ahead and feed then settle her back to bed (ok if she feeds to sleep on those occasions), and make a note of when 4h later will be. If however she wakes and it is BEFORE 11pm you do not feed her, but you use shh pat/PUPD to resettle her all the way to sleep, even if it takes hours and even if it takes you past 11pm. You can then feed at the next waking (as long is it is past 11pm!), and calculate when your next 4h mark will be. Does that make sense? The idea is that she learns that protesting for long enough doesn't get her a feed, but that she feeds when genuinely hungry.
Sleeping out and about is a different question......honestly I don't think there's a lot you can do about it if your LO isn't a car/buggy sleeper. Mine never was, unless completely and utterly exhausted from about 4 months of age. I plan my days around nap time and make sure we're home in time for sleeps. It's hard in the early months as they need naps so often, but it gets easier as they can stay awake longer. Of course there will be days when you just have to get out for whatever reason, and on those days you need to accept LO will probably get OT and early BT can help x