You are not, not,
not a horrible parent!!! (((((hugs)))))
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You are a wonderful mommy who just wants her baby to get some quality rest! And you need rest too to be the best parent you can be.
30 mins naps really sounds like overtired, I hope that getting her onto a routine can help her to be better rested! With the routine, the last feed would be right before bed (sorry I missed that E out!)
Shush pat and PUPD aren't really separate techniques, they sort of merge into one another, and you need to find what works for your baby. Here's what I would do:
Work out a little 5 minute wind-down routine that you can use before every nap. Write it down and stick it to the wall in her nursery so that everyone can follow the same steps in the same order. The wind down won't make her drowsy, but it will soon become a cue for her that she'll be going to sleep soon.
Then put her in her crib. Try to use shush-pat in her crib to settle her. You may need to find another variation, like no shushing (sometimes they hate it), or stroking her back instead of patting, or patting her butt, or jiggling the mattress - whatever works. If she gets furious and pushes you away, maybe you would just rest a hand on her back.
If she just gets more upset and shows no sign of settling, pick her up, hold her for just a moment while you say your key sleep phrase (this is the phrase that you will say at every sleep time, something like 'it's time to sleep now darling, mummy's right here), then lay her back down again immediately, even if she's still crying. Then try again to settle her in her crib.
Some spirited LOs can't handle any intervention, and any attempts to help them settle will make them furious, and picking up makes it worse. For them you might just stay with her while she cries. This is NOT the same as CIO, because you are there with her and will help her any way you can.
When she's totally calm, you can start to gradually step away from the crib until eventually she is falling asleep by herself without you in the room.
The nights is a tough one to call. I would probably feed if it longer than 4 hours since her last feed. If it is less than that, resettle back to sleep using PUPD. If she wakes at 3hrs, keep going with PUPD until she sleeps, even if that takes you past the 4 hour mark. Then just feed quickly, quietly, in the dark, at the next waking. I guess I'm saying to decide whether you're feeding or doing PUPD before you go in to her - don't start with one then switch to the other.
I hope all this makes sense!!
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