Hunny I've been there a few times with DS.
Could you put her in the sling & go for a walk with a brolly?
I know its wet & sloppy out there (is here too) but being outside might distract her enough to doze of while she's close to you.
I had a similar prob a few days ago & the only way I got Jesse to have two 10 minute naps was to walk with the sling & just sit as still as possible til he woke up. As I said...10 minutes.

I hope something works soon.