My wife and I disagree about this. I think it's a bit selfish and neglectful to leave her alone, especially when for the first 20 minutes she just cried and screamed. After that she was pretending her doll was her baby and feeding it and burping it. This indicates she feels a little abandoned and is looking for something to love her, even just an inanimate doll. Am I reading too much into this?
I think you are reading too much into it. Your three-your-old calmed herself down and contented herself with quiet play instead of napping. She is playing with dolls because that's what many three-year-olds do. And while she wasn't napping, she was having quiet play which is a restful alternative. The ability to entertain oneself is an important life skill!
Let me provide a few separate comments:
"When you assume, you make an ASS of U and ME..." <-- I'm just saying that assumptions are often misleading, and discussions help!
First of all: playing with a doll pretending to burp it mother it in any way is normal three year old behavior and is perfectly healthy. It by no means indicates your daughter is feeling abandoned. Hopefully knowing that can help you to relax that your child is not/has not recieved long term damage from your wife.
As long as the child is in a safe environment free of access to dangerous tools and the like, it is considered pretty healthy for a kid of your daughter's age to be required to have some alone time (while a guardian can still hear if there is trouble). This is time for a child to decompress, learn how to self entertain and drift off to sleep if he/she is particularly tired that day.
At three, she finds hanging out with mommy more interesting than sleeping. Since she is also at an age where she may suddenly be needing a little less sleep, but might still need the nap on some days while not on others, she may be contending with learning how to play by herself/soothe herself, etc so she is protesting loudly - another normal three-year-old behavior.
Going to a screaming child and letting it get its way is a good way to encourage the screaming and yelling to continue. Your wife is probably trying to make the point to your daughter that her naptime is supposed to be alone time, and she needs to accept it. Going and discussing the idea with your daughter, probably only makes the time of protestation last longer in the long run (at the age of three - I would speak differently of a child that is younger).
Having said that, there are some preventative measure you can take so things start off well instead of with screaming. If you or your wife, aren't already, I suggest:
Selfishness can also be referred to as "self care" when in balance, and requiring your daughter to have some quiet time and/or a nap (which is also healthy for your daughter) seems perfectly in balance to me - people who have a job, "at the office" get a coffee break, the ability to use the restroom without a little one staring at them or banging on the door AND a break for lunch - your wife doesn't get any of those things. Even the best, most devoted moms need a little time to themselves - something most three year olds are extremely reluctant to give for more than about sixty seconds (and even that is if mom is lucky) without mom forcing the issue a bit. To help your wife get her personal needs met too, you need to consider her needs just as important as yours and the needs of your daughter's. If your daughter is dropping her naps, your wife is probably getting even less down time than she was previously getting. Perhaps, if you aren't already, you could step in and take over on an afternoon every other week or weekend so your wife can have some girl time with friends or some down time of her own too.
In agreement with Mary Jo's answer.
Children will play with their toys, pretending to feed and burp a doll does not mean a sign of neglect or abandonment, it has been a tradition of girls for generations and plays a part of role play, conditioning and preparation for a particular role as a parent (much as lion cubs play fight and hunt each other in preparation for hunting as adult lions).
Many mother's crave sleep (as do father's) and provided the child is safe, there should be no harm in a parent napping. Given the scarcity of details it would be hard to comment on much further on the situation. As to where your child is while your wife is napping. I would nap on the couch while my son was playing beside me (if he wasn't napping), that way he was supervised, as I would not go into a deep sleep when napping like this.
So with the issue of safety and neglect out of the way, I think we need to look at the more important issue.
Disclaimer: Please I stress, it is good to come here with questions, I am making an observation of what may be a deeper cause.
This is not a good sign to be bringing a he said she said type of post into a public forum. There are many ways to cloak a question without it being a direct reference to such a source of conflict within a relationship. As internet strangers cannot adjudicate between the two of you and decide what is right or wrong here, as we do not really have the full picture. My way of thinking this indicates that the issue that needs to be addressed is the communication between you and your wife.
Parenting puts strain on both parents, it tests a relationship and totally changes the dynamics and expectations between couples. It's a huge adjustment and can remain so for some time. For some couples it is not until the children are at school that they work out some harmony and synchronization with child raising.
The real issue here is for you and your wife to be able to communicate, her needs and feelings of fatigue and how these can be addressed, without recrimination over parenting. When my son was a baby, an old friend would say to me, for a happy child make a happy mother. I think there is a lot of wisdom in this; except of course this extends to fathers and all care givers. The primary care giver, is the one who spends the most time with a child (obviously, by definition), and as such, it pays dividends to look after this person, in the overall picture of caring for a child.