One of my sons came home at the age of 20 months when his 'big' brother was only 23 months of age. The 23 month old had never gotten reliable about sleeping all night. The newest arrival woke crying in terror several times a night due to the huge change in his life. AND they slept in the same room, so they would sometimes wake each other.
I was pretty tired for awhile. I put a mattress on the floor of their room, so that when either boy woke, I just went in and laid down with them. The better-settled, older child would go back to sleep right away, but the younger one often needed me to pat his back for a few minutes to settle back down. I know that some folks just turn on the TV when their kids awaken them in the night, but I don't. I keep it dark and stay close.
When parents get really exhausted, it can be tempting to go the cry-it-out route to teach toddlers better sleep habits. I am not at all convinced this is wise for newly arrived adopted kids. I much prefer the cry-in (mom's arms) method. Let me explain.
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My first daughter from Ethiopia was 20 months on homecoming. She really seemed to resist sleep in the first weeks home. She would flip and flop and play and fuss, but she didn't let her body be STILL enough to go to sleep. One of the first nights I had her, (when we were still in Ethiopia, in fact) I KNEW she was exhausted. So I just sat in bed and held her in a cradle position, not letting her get up. She howled like CRAZY for 7 minutes (I know, I was timing it) while I rocked her and sang to her. Then, abruptly, she gave up and went to sleep.
Probably a dozen or so times after she got home, she would get in that 'resisting sleep' mood, and I would just hold her and rock her and every time it took less than 10 minutes of crying and she would give up and go to sleep.
I fell that crying in a separate room alone could be harmful to newly arrived, unsecurely attached kids. However, crying IN mom's arms while being rocked and caressed is a totally different thing emotionally. And in that context I think that the crying actually let my daughter 'cry out' some of her stress and settle enough to sleep.
The most important thing to remind yourself when you are in the pits of sleep deprivation is that this is temporary. In six months things will probably be getting better. By the time your child has been home a year, most likely the sleep issues will be almost gone. But for now just take it one night at a time.
Try to get to bed early when you can, and really take advantage of the times your child sleeps. Nap, if you can. Get some exercise every day. Eat some chocolate every day (it's medicinal, you know!) And remind yourself that things WILL improve eventually.