This totally sounds like our story. First and foremost, get rid of the "Pack n' Play". We found out the hard way, none of our kids liked sleeping in them. These don't offer enough support to give the baby a sense of security. We had great success with a portable crib we purchased through Toys R' Us online. This was about 2 years ago, so I'm not sure if they still carry this. But it is made by a company called I Luv. It's the same size as a pack and play, but it sits high like a regular crib, is wooden, folds flat, is very portable, easy to open, has a mattress, the stability and depth of a good crib. Our kids could sleep peacefully in this. If you can't find one at TRU, just do a general search on yahoo or google for "portable crib" and you should get a great selection to choose from.
Second, if your mother-in-law is like my mother; over 60, well-intentioned, but lacking the patience of a young mom, the baby is probably picking up on her tension and anxiety and is not feeling too comfortable around her and may be fussy or edgy around your mil.
Face it, she probably doesn't have the stamina she used to have to manage a demanding baby, and the day to day drill of changing diapers, feedings, and providing stimulating play is alot for her to manage. She probably has too much pride to tell you this is where she's at, and would rather just tell you she's raised two of her own instead to get you off her back. She's probably feeling a bit stressed about this, and is super sensitive to anything you might say, even if it's helpful. She feels she doing you a favor and doesn't deserve to be second guessed. She's probably taking the baby to her old office or avoiding naps because she's looking for solace or a diversion to help get her through.
The only way this will continue to work for you is to lower expectations somewhat and let her call the shots, or perhaps look at this as a short term solution and be looking for a more objective party to watch your baby.
Just keep in mind if there's tension and no seeming relaxation on either side in the near future, this probably won't last long before there's a knock-down ideological blow out over something totally stupid like whether she put the baby in a onsie versus a t-shirt. Just remember, she's going to save face, and make you the villan. She won't want to admit she failed, let you down, or is just (gasp!) too old to take care of a baby.
If you really are financially dependent on her helping you out, I'd pick my battles carefully.. and be prepared for the inevitable. Do yourself a favor, and either bite your tongue (unless the baby's in danger) or take her cues that she's probably not up for the challenge, and is hoping you'll get it and find another day care solution soon.