I would also suggest enrolling her in preschool 2-3 mornings a week. My son started at age 2 because he is so active and his brain and body need to be engaged all the time. We were also expecting his little sister and I had SEVERE nausea and vomiting through my 7 month of pregnancy. So at 4 months of my pregnancy he started preschool. He thrived there and still loves it!
Is there anyone closeby that can babysit her for you for a couple of hours a day? Someone who can take her to the park or maybe to a parent and child type class during the time that you other child naps? That could be special Grandma or Grandpa time for her. Or maybe if you hubby can rearrange his work schedule, he can take her out for some special Daddy-Daughter time twice a week during that naptime? Sometimes my hubby would pick up my son from school at take him out for lunch or even to run an errand.
What we did when my son started phasing out his nap at age 3.5 years was to still have quiet time for him. My 2 yo daughter still naps from 1-3pm. I make my son have quiet time in his room from 1-2pm. Then he can come out and play quietly in the living room, watch some tv, play video games, go outside and play with me, or do some sort of indoor activity with me and I know that my daughter is well into her nap so a little noise won't bother her.
One thing that we did when he was a little younger was what we called the "Fun Jar". If he did his quiet time nicely, when he came out he could pick out something from the Fun Jar to do. I cut up strips of paper and wrote activities like:
play xbox games
play with sidewalk chalk
Mommy reads a book
Pillow pile where we bring out all the pillows and jump and roll around on them
Set up a table fort with blankets and towels
have a special snack (candy, fruit snacks...stuff that he doesn't normally get)