Sometimes, there's just no replacement for Mom, expecially if she's had a cold. To some extent, it's a phase. To another, there will always be times that it's gotta be Mom. There are two issues here: her relationship with her father and your sleep.
At 9 months old, I still can't leave DD with DH so that I can sleep. It's probably mostly my personality, but I can't sleep if I can hear her, happy or not. My saving grace is the fact that babies sleep a lot, not necessarily a lot without waking up, but a lot total. When I get behind on sleep, it might take me a couple days to catch up, but if I religiously lay down and rest, sleep if I can, every single time DD sleeps, I can get more than enough sleep.
There's this nagging feeling around that age for a lot of people that she should be happy with her daddy. After all, he's a good daddy, and I want her to love him like I love him. Well, the fact that she's unhappy with him now is normal and not a reflection of how her relationship with him will always be.
Leaving her to cry in her daddy's arms is not a mean thing to do. You are not abandoning her with no support. You are leaving her in the arms of her father who loves her very much and is doing everything he can to make her happy. It may not be as often, but there are times that she cries in your arms too, and you are doing exactly what you should do to keep holding her. If you NEED a break, take it if it will make you a better mom.
I resorted to this as the most loving answer when I needed a moment to myself from time to time. Especially when it was late at night, and we were both tired and I had been walking her and bouncing her for an hour while she cried on and off, and I was getting stressed out, and I'm sure she could sense that, and it was only making it worse.... I would give her to her daddy. The screaming would escalate. He would take her out of the room, and I would pray/meditate for just a couple minutes until I was sure I was ready. It gave me the strength to calmly and lovingly meet my baby's needs so that she could go to sleep. I have no regrets.
At the same time, those were not DD and DH's best bonding moments. Things got better when I gave up on the idea that it all had to be fair. (Actually, I'm still trying to give up on that idea.) We searched for a way that DH could have some quality time with DD. We found that in walks. The two of them could go for a 15 minute walk around the block (Blocks are big here.), and she would be happy for that time. The two of them could bond, and I would get just a bit of a break. (A friend of mine's husband bonded with his daughter through infant massage, and now she sleeps on his chest at night.) Slowly but surely, Daddy became a very fun playmate. But... there's something really special about Mommy... probably the boobs!
