At 10 weeks old she is still in the "4th trimester". She needs wants, needs and craves the comforts of the womb. That's why she wants to be close, that's why she wants to be held and that's why she hates her crib. Google 4th trimester. It will give you some great info on why she has some of the behaviors you are seeing.
She is far to young to try to sleep train. So the putting her down drowsy thing has no meaning to her now. She doesn't get it. She's running purely on instinct at this point. She has no concept of day and night.
You can start night routines so that when she's old enough she will be able to start to "get it". Babies thrive on routine. They learn what to expect and what is expected.
Make sure you swaddle her before getting ready to get her to sleep.
She may have a bit of reflux which will make it difficult for her lay down and be comfortable. Try a sleep wedge like this one:
http://www.toysrus.com/product/index.jsp?productId=240184...
I still use it with my 2.5 year old when she has a cold so it's def. worth trying as it can be used for a variety of things and for a long time. And it fits tightly under the sheet and is the same width as the mattress.
Try a white noise machine.
At this point you can't expect her to sleep thru the night (and that means a 5 hour stretch). She can only do what she is physically and neurologically able to do. But you can try the above to make her more comfortable and possible get better sleep.
Dr. Sear Baby Sleep Book has some great info on infant sleep and I personally found the more I knew and understood infant sleep the better I was armed to teach my 1st how to sleep when he was old enough. The Baby Whisperer also has great info and tips along with The No-Cry Sleep Solution.
And always remember that parenting never stops. Doesn't stop because we are tired, sick, have to get up early in the morning, have to go back to work, have a date night planned, it's nighttime. I always tell myself this when things get hectic or frustrating.