By trying "wild card" searches you can sometimes get around different spellings of
names as well as misspellings and bad transcriptions. I did a search for Dora
Mol*sky in Ancestry and found your family in the 1920 US census indexed as
Molbawasky. I also found them in the 1925 New York census indexed as Moldofsky and
Moldopsky. The 1920 US census particularly contains a lot of useful information that
should help your search. I couldn't find them in the 1930 census but if you persist
with different strategies you will eventually succeed.
Good luck with your search.