Margot - I would definitely suggest having the cot in your room to begin with. I have found that with big changes, small steps is the way to go. Whilst Gabby has always slept in her own room, whatever changes I have made have been in small stages. For example, we are in the process of trying to get Gab to sleep unwrapped as she has been wrapped since birth. I have started putting her in a sleeping bag at night only (as this is when she is more tired and able to fall asleep without distractions) and it is working so far. She's waking up more than if she was wrapped but it's getting better. Once she has it down pat, I'll start putting her sleeping bag on for her day-time sleeps too.
So, perhaps you could just do one nap in the cot to start off with? Or, because she is used to that swaddled feeling, wrap her tightly to sleep in the cot with a muslin or cot-sheet?
My mother is angry that I'm even considering putting her in her own room so soon, as she says that it's dangerous.
I honestly don't see how this is so..... as I said, Gab has been in her own room since we brought her home (we just couldn't sleep with her in the same room). We have a monitor so we can hear if she needs us. Don't let your Mum bully you - you know what is best for you and your child. The last thing you need is a guilt-trip put on you when it's SO obvious you are doing a magnificent job!