I don't have much advice or anything other than I think it sounds like YOU really trust your mom and that's important. And I do think one night of sleep can be wonderfully recharging. The other day, after waking up every hour or so and taking 1/2 hour to get back to sleep from 2am on, DS suddenly fell asleep at 8am and napped for three full hours. I was still in bed with him (hadn't gotten up yet) and I got to sleep too. I felt fantastic for the rest of the day just having gotten three solid hours....
Also, I was reading an article in Psychology Today about sleep deprivation and how it inhibits a person's ability to recognize differences in body language and facial expressions. The interesting and pertinent thing about this study was that after even just ONE night of uninterrupted sleep, the people in the study were back at the same level as someone without sleep deprivation.
I think even if you don't FEEL completely restored body and mind, it would probably do you more good than you realize.
Also, I posted this** in another thread. It's some advice that a facilitator at my mom and babe group gave. I haven't tried it but some of the responses to my post had and said it worked for them, so maybe...
**One thing she said was for babies that have REALLY short or seemingly non-existent deep sleep cycles (who seem to constantly be in shallow sleep and therefore wake easily and often), she recommended spending a few days really watching them sleep and as they come out of one sleep cycle and SEEM to be waking to take that moment to place a hand on them and jiggle softly or whatever seems appropriate and try to get them back to sleep before they come totally awake. If you can manage to get them back to sleep without picking them up and if you do this often enough, hopefully they should start sleeping longer. The theory here being you are helping them learn to come out of a sleep cycle and enter into another WITHOUT coming fully awake.
The other thing she recommended was if they do fall asleep somewhere (like in the carseat or the stroller) on a fairly regular basis then you can build a routine off of that. So for example, if your baby sleeps in the stroller when your go for walks, start going for a walk everyday at the same time. Once your baby is in that habit, start placing your baby in the stroller and not going for walks, just rocking it a bit until baby falls asleep (or the whole time baby is sleeping if s/he keeps waking up when you stop at that point) and them progressing to just putting baby in the stroller to nap without rocking it, and so on... (I don't know if this would work with a carrier because I think it would be more difficult to transition away from mommy's bodyheat/smell/movement).