I can't speak for recent death certificates >from Florida, but you are
in luck regarding NY City death certificates. If the death occurred
1948 and before, they have been indexed by ItalianGen.org and are
available for free via email through FamilySearch.org

The documents include a location for parents' names. Whether the info
was provided or is correct, is another matter.

The index on ItalianGen.org indicates that Yetta Covell was 74 years
old when she died on 27 Dec 1943. Her Death Certificate number 26943
was issued in Kings County (Brooklyn).

At this point you may order it via the New York City Municipal
Archives for a fee or through FamilySearch.org for free and receive it
via email.

If you choose FamilySearch:
1. Click Search at the top of the home page
2. Click Catalog (since I already know this dataset has not been
digitized and is not online)
3. Place name: type in Brooklyn
4. Select New York, Kings, Brooklyn
5. Scroll to very bottom of page and select New York, Kings, Brooklyn
vital records (9)
5. Select "Brooklyn death certificates, 1919-1949"
7. Using the certificate number and year of death, scroll down to see
which microfilm would have the record
It appears to be on microfilm 2166405, item 1

Now go to FamilySearch's Photoduplication Services and order the
record. Make sure to give them all the information you have about the
record and especially the person's name, date of death, location of
certificate, certificate number and the microfilm number.
The instructions are at
https://familysearch.org/learn/wiki/en/Photoduplication_Services

I have walked people through this process for other types of records
in a blog post at
http://extrayad.blogspot.com/2013/01/fee-records.html
Use the links in this posts to other posts on my blog to get the full
story on how to acquire records >from FamilySearch.

By the way, a better source for mother's maiden name might be a
child's marriage certificate. I looked up Lena Covell on ItalianGen
and found a marriage (about the correct time period) to John F Wolf.
There's something wrong with this index, however, since Lena and
John's marriage date don't match. You might try looking for marriage
records for Yetta and Morris' other children on ItalianGen. Cross
check the marriage date with the point at which the child disappears

from Morris and Yetta Covel family census records. You may then

acquire the marriage certs using a similar process via FamilySearch.

Both FamilySearch and ItalianGen are fantastic resources for NYC research.

Emily Garber