hmm I agree with pps that your mom should work around your LOs routine and that sleep IS probably better in the cot, BUT I also understand the need to get out of the house. We go out everyday, after nap 1 and we come home before nap 2. We do lunch (solids) out-- I go for a coffee with dh or friends or just with ds. We live in the city and it's a short walk to the oldtown pedestrian zone, so it's perfect for a stroll. I do find that we do need to spend a bit of time at home before the nap (or more time at home before we go out) in order for him to have 'floor time' playing, crawling, cruising...using some energy iykwim...
We have a short am nap (I wake him at 45) so IF we have to be out for some reason, he can sleep that one usually out in the stroller-- because when he does sleep in the stroller it's never usually longer than 35-45 minutes. But it IS possible, if we're out and it's naptime, it may take him a bit longer, but he does go to sleep... just for not as long (and probably not as restorative) but once in a while, it's ok..)
didn't mean to be so long! Good luck!
Kristi