I have taken my charges to the mall, but only when I needed to buy something for/with them.
On the other hand, I have never, NEVER had a parent complain that their children were out of the house too much.
Just for comparison, this is a once-per-week schedule that I had while live-in 24/7 homeschooling 7 children ages almost 3, new 5, almost 7, 8.5, new 10, new 12, and almost 15 at the start. Nobody napped, and the kids did school 5-6 days that we didn't go to town.
6 am youngest 2 got up and around with help
6.15 am next 2 got up with supervision
6.30 am last 3 got up while I made breakfast with younger kids helping
7 am breakfast
7.30 am dishes/chores
8 am kids in car, driving to town, drop books in library slot on the way past
8.45 am park car in middle of town, walk to park (decent weather) or town rec center
9 am playtime
10 am walk to library
10.15 am choose new books
10.30 am storytime (several book, music/dancing, craft)
11.30 am walk to car, drop off books, pick up lunch
11.45 am walk to park or rec center
noon lunch and play
2.45 pm walk to rec center if we were at the park
3 pm homeschool gym group
4 pm walk to car, drive to store
4.15 pm weekly shopping
5.15 pm load groceries in car
5.30 drive to park/rec center
5.45 pm dinner
6.15 pm drive back to house
7 pm arrive home, unload groceries
7.15 pm youngest got ready for bed
7.30 pm youngest in bed, next two got ready
8 pm 2nd and 3rd in bed, next two got ready
8.30 pm 4th and 5th in bed, next got ready
9 pm 6th in bed
9.30 pm last got ready
10 pm 7th in bed
I carried a backpack with snacks, books, toy and a change of clothes for the youngest. Everybody (including the youngest) had a water bottle in their backpack, everybody except the youngest also carried a toy and/or book to read if they were tired in their backpack. There was a second bag just for library books going back, that way we didn't need to pack and unpack bags during the day. Water bottles were refilled as needed, bathrooms were always available, kids loved it (oldest wasn't enthused about the gym group). Parent was very in favor of kids being outside as much as possible, and if not outside, at least running and walking around.
When the temperature dropped below zero, we drove rather than walking.
When I started with 15 month old twins, the schedule was (for a short time, at the parents' insistence):
7.30 am up, diaper, and dress
8 am breakfast
8.30 am clean up
8.45 am diaper and brush teeth
9 am playtime outside, incorporating early education
10 am in stroller for a walk, snack in stroller
10.30 am transfer sleeping child to crib for nap, try to do a diaper change without waking the child
12.30 up and diaper
1 pm lunch
1.30 pm clean up
1.45 pm diaper and brush teeth
2 pm education focused playtime in the basement
2.30 pm snack
2.45 pm reading/playing in bedroom
3 pm diaper and back to reading
3.30 pm snack
3.45 pm reading/playing in bedroom
4 pm diaper
4.15 pm either mini nature walk outside or unguided playtime in the basement
5 pm dinner
5.30 pm clean up
5.45 pm teeth, bath, diaper and pajamas
6.30 reading/playing quietly in bedroom
7 pm bottle (drowsy or they wouldn't take it)
7.30 pm bedtime (rocking to sleep, children would wake when put down, so they usually fell asleep after 8.30 pm)
The parents were too focused on limiting germs by not going ANYWHERE, too much food too close together, and nap was way too early and started in the stroller. We transitioned to naps in the crib first, then bedtime in the crib. By gradually shifting the nap later, snacks and lunch were spaced more reasonably. However, the mother was overly cautious about injury and illness, so the kids never socialized with anyone other than relatives while I was there.
I'm not saying that there can't be a middle ground. OP, you need to talk to your nanny and figure out what will work for her and your child. I would NOT recommend limiting outings to 1.5 hours at 16 months, because at that age, your child needs to walk as much as they can before finishing the walk in the stroller.