Sleep Crisis with 21-month old daughter

My wife and I have a problem which shouldn't be a huge crisis, but has
turned into something terrible.

When we adopted our daughter almost 2 years ago, we used the Dr. Sears
book as our main guide and so our daughter has always slept in our bed
and although there have been some issues, this has worked out somewhat
until now. I should also explain that she does not know how to lay
down on the bed and fall asleep--we have always walked her down and
carried her to bed after she has fallen asleep. I now believe our
whole approach was deeply flawed, but still we have gotten by so far.

Then I caught a cold and a few days later (naturally) all three of us
had it. Then my daughter started changing her normal way in bed.
Usually, my wife carries her into the bedroom about midnight (way too
late, I know) and lays down on the bed with my daughter laying on her
shoulder for a few minutes, then shifts her off her shoulder onto the
place next to her. The problem is that my daughter is now being very
resistant to being shifted onto her own place on the bed. She may wake
up during this shift and start crying and demand that my wife pick her
up and carry her around. Or she will make the initial transition, but
will wake up a couple hours later, start crying and demand that my wife
pick her up and carry her around. When you pick her up and walk her
around she seems to sleep on the shoulder. But then when my wife tries
to get back into bed, either my daughter wakes up and again cries and
demands to be picked up and carried by my wife, or, successfully makes
the transition to her own spot, but wakes up 2 (for example) hours
later and goes through the whole rigmarole.

When my daughter cries for this it is not just a whiny demand--she
seems genuinely distressed. I have spent several mornings carrying her
around from 8am to 10 or 10:30 (about her normal get up time) so my
wife can sleep uninterrupted those last 2 or 3 hours but this is taking
a toll on me. When I try to lay her in the bed when she seems to be
sound asleep in my arms, this is usually unsuccessful (strangely, I
have pretty good success at doing this in the afternoon when putting
her down for a nap).

It seems to me the solution is going to have to involve letting her cry
for some time when she wakes up and does this (by the way, she still
has a little bit of a cough and stuffy nose still, but her cold is not
particularly bad now). My wife is very hesistant to let her cry (as am
I) but we need a real solution that 1) works, and 2) does not
traumatize our daughter.

I am appealing to anyone with a solution or suggestion on what we
should do to get help. Thanks.

Paul