I didn't set out to parent with an AP ethos, but that's how it's worked out because my twins settle so quickly if you respond quickly, sleep much better in my bed etc, so it is what works for us.
Also as a happy coincidence, we've spent a lot oftime with my mum, in our house. I have also left my babies with my mum for short periods of time from a few months old. Because my mum is often around, and when she is we effectively co-parent, popping in and out of rooms, passing babies back and forth etc, they have become pretty much as attached to her as the are with me.
I left them overnight for the first time last week - they're 13 months. They generally cosleep, feed to sleep and feed 3 or 4 times each in the night, so I had no idea how mum would cope with them overnight (in our house). She put them to bed in their cots and try went to sleep, she lifted them for a cuddle on the 1 occasion they each woke and then put them back in their cots, and she didn't need to offer milk in a beaker overnight as they just settled.
I guess what I'm trying to say is that I wholeheartedly agree with AP methods of parenting. But to avoid a distraught daughter, can you get your mum to spend time with you, at your house, taking a completely active parenting role while you're there? Then she may become as interchangeable with you are my mum is with me. I have suffered your mum - obviously this could be your DH, but they tend to work during the day, and personally I think they become exciting people who are there at weekends and sometimes in the evening. What you're looking to develop is a very close person for your daughter, who is as normal, mundane and boring as you are 
Good luck. Personally, I wouldn't change your parenting and cause distress to your daughter now to prevent a bit if distress at some notional future point that you might have to leave her. She might surprise you next time and sleep well like my two did 