My daughter was 3 going on 4, when I had my 2nd child. Her little brother.
Before I had him though, 'naps' were a daily routine. She napped.
So then once her baby brother came home, 'naps' were still a routine.
And I explained to her.... what a baby is, and that they nap too, and that Mommy 'naps' too because the Doctor said I have to rest. (I had had a c-section) etc.
So I explained all of this to her. She understood.
I synchronized, the afternoon naps to be at the same time as her baby brother.
And I rested too, at that time.
I would ALSO say, that "it is Mommy's nap time too.... and baby brother..."
That worked for me.
3 years old, is not an easy age. Developmentally.
So keep 'expectations' age appropriate, or the child will get frustrated, and you too.
My daughter, even at that age, understood that when someone is sleeping, it needs to be quiet.
We tip-toe, whisper, and make quiet.
I explained that to her. That she can talk, but has to 'whisper' and tip-toe in the house. And I would, show her how. And that Mommy did that too.
I explained to her, all along and each month, what a 'baby' is and how they are developing and what they can or cannot do. That a baby cries/i nurse him/they wake etc. But it is Mommy's 'job' to take care of baby, and she does not have to feel, bothered by it.
My daughter understood.
Because, instead of expecting her to just understand.... I approached it as... this is all 'new' to her too. The baby. Thus, I simply explained things to her. A child does not understand 'why' unless you explain to them, and incorporate their own age-related development, too.
In the afternoons, was QUIET time in our house. It was a DAILY routine. Thus, my older daughter knew. Because it was just routine.
I would lie down too, on the sofa etc., after I put her baby brother to nap, and then I would put HER to nap. That was my 'sequence' of it... and putting my kids to nap.
Anyway, that worked for me.
My son is 4 now and still naps in the afternoons.
My daughter even if she is 8 now, will still nap in the afternoon is she is tired.
Because, it has always just been the 'routine' since they were babies.