(((Hugs))) sorry you're having such a hard time! You've come to the right place to get some help!
Could you post your routine so we can have a look at it? Could be your LO needs more A time.
About the sleeping: ideally you get her calm and settled, put her in the cot and then leave her to fall asleep on her own. I found that as long my DD isn't fussing or crying, it's best to leave her to it and only intervene when she needs it. I've never really used PU/PD, but it's my understanding you only do it when LO is really crying. As soon as LO is mantra crying you put her down and see if she'll settle on her own.
If she doesn't settle on her own, you should always try to settle her in the cot as your aim is to teach her to fall asleep independently in her cot. You could do ssh/pat or the version you are using if that's working for you. She might become dependent on you to shh her to sleep, but that's something you can gradually wean her off. It's something you control and therefore it's not a prop.
If shh/pat doesn't help you do PU/PD.
Regarding the rolling about: there's not much you can do about that besides giving her enough tummy time during the day and trying to show her how she can roll back.
If you can, try not to obsess too much about the naps and extending them. I know it's hard not to.
I got the dreaded 45 min naps after 3 mo as well and finding the right A times together with W2S is what helped me out the most. But I was constantly stressing about them, stubbornly trying to extend and ended up spending most of the time in her bedroom. After some time I decided to go with the flow a little bit more and now I'll only try to extend for 10 min or so. If I see she's too awake, worked up,... I just get her up and give her a shorter A time before next nap. That helped me to keep sane!
I'm not saying this is how you should do it though, just make sure you're having fun with her as well.
What city did you move to? Must be hard to be away from friends and family.
Barbara
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