As a mother of 4 children, I hate to tell you this.......I had two children that took naps up till they were 4 and then I had the other two, one was really bad. She was never a sleeper and still isn't to this day.
20 months is awfully young to reason with, I would make a point that he had to stay in her bed for 1 hour each day, yes I'm sure there will be crying and such but after awhile she will get use to it. I would also allow hard back books in her bed too.
How much does he sleep at night? Maybe less time will mean a longer nap in the afternoon. Keeping in mind a toddler requires more hours of sleep.
I know this doesn't help but been there, good luck.