I hope you find a solution soon
can you bring her into bed with you, or put a mattress on the floor of her room? 2 is a big separation anxiety time and it sounds like she needs you.
Wrt bedtime I don't think your dd is manipulating you, just expressing a need, and the sooner you address the need, the sooner it should pass.
As for the other tantrums, I think it's pretty normal. I encourage dd to take deep breaths which works well for us, but she's just shy of 2.
Sunshine, our pair of girls are very similar ages (DD1 is a bit older though - 2y 8mo, DD2 - 3mo) and I went through a very similar thing when DD2 hit 2 months. It was as if the jealousy of having a sister didn't hit straight away as we had 2 months of joy with DD1 very happy to have a little sister and being a delightful 2 year old then BAM! Overnight DD1 turned absolutely feral! It was as if her terrible twos, sister jealousy and a developmental milestone tantrum were all rolled up into one. I was floored as I had never had an ounce of trouble from DD1 before.
Defiance, waking constantly at night and being disagreeable. It was really, really, really tough and I feel for you.
I tackled the bad behaviour by treating DD1 with as much love, patience and time as I could muster (some days I had more than others admittedly) as I figured she was testing my boundaries and love for her now there was a new kid on the block. I also remained firm on non-negotiables and would take her to her quiet spot (pile of cushions in her room in a nook) when she was tantrumy eg refusing to go down stairs without being carried - something I could no longer do with a baby in my arms. She had to stay there till she was ready to listen to me and talk to me by telling me her story - ie me listening too (my version of the naughty chair, I hate using the term 'naughty') I never time it, just keep going in to see if she is ready to talk and I tell her its ok to cry/make noise if she feels she needs to, we just can't talk till she is calm. This took about 2-3 weeks to work and it was a hellish time. I didn't get anything done, the house was a mess and many times DD2 had to just make do or was pulled off the breast too early so I could deal with DD1. I'll admit that I wasn't always calm, but... it has worked. She is so much better now and if things get heated, I just ask her if she needs to go and have quiet time in her room and she usually listens to me properly on the spot now.
With the constant night time wakings I figured that it was DD1s way of making sure that I still was there for her, DD would always yell for me and refuse comfort from DH. DD was waking 3-6 times a night and refusing to go back to sleep (She doesn't actually get out of her bed but will call and cry until we come in.) Some times she would be awake for 3 hoursAgain it was hellish and exhausting but I would go to her when she called and cuddle her if she wanted it. I would always explain to her that I am always here for her but she needed her sleep so she could have fun tomorrow and I also needed to get my sleep so was going back to bed. I would check she had all of her comforts, music on, teddies, blankie etc and then resettle her. If she kept calling, I kept going but warned her I couldn't keep cuddling her and would just come to the door to check on her. I would always try to remain calm (!). The bad nights were the ones which were bookended by DD2 waking and needing a feed. It is working though, the wakings are less frequent and I really believe it is because DD is getting better adjusted to the changes going on around her.
Sounds like your smart little cookie is a bit like mine. Well aware of all of the changes and trying out different ways to make sense of her new situation. Hang in there and keep digging into that reserve of love. Make sure when your DH is around he takes both girls off your hands so your can recoup on loss of sleep.
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