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I am Nigerian. My family went on a trip to USA from Nigeria in 2013 and came back together. Recently, my mother applied for another visa and was refused because, according to them, my sister is still in the US. They didn't stamp and acknowledge her exit. How do we rectify this, as it will affect her travel and, apparently, that of my family in the future?

You can check her i-94 from here i94.cbp.dhs.gov/I94/#/home. It should have her arrival and departures within the past five years. If it is not recorded you will have to submit evidence like plane tickets, boarding passes, etc things which can confirm she was OUT of the USA by the deadline. The onus is on you to gather overwhelming evidence, then you. You can then submit that evidence by the method and to the address shown here

I forgot to turn in my I-94 when I left the U.S., what should I do?

If you failed to turn in your I-94 Departure Record, please send it,
along with any documentation that proves you left the United States.
As of November 1, 2014, the address is:

Coleman Data Solutions

Box 7965

Akron, OH 44306

Attn: NIDPS (I-94)

USA

(If using U.S. Postal Service)

OR

Coleman Data Solutions

3043 Sanitarium Road, Suite 2

Akron, OH 44312

Attn: NIDPS (I-94)

(If using FedEx or UPS)

Do not mail your Form I-94 Departure Record or supporting information to any U.S. Consulate or Embassy, to any other CBP Office
in the United States, or to any address other than the one above.
Only at this location are we able to make the necessary corrections to
CBP records to prevent inconvenience to you in the future. Coleman
Data Solutions does not answer correspondence, so please do not ask
for confirmation that your record has been updated.

To validate departure, CBP will consider a variety of information,
including but not limited to:

Original boarding passes you used to depart another country, such as
Canada, if you flew home from there;

Photocopies of entry or departure stamps in your passport indicating
entry to another country after you departed the United States (you
should copy all passport pages that are not completely blank, and
include the biographical page containing your photograph); and

Photocopies of other supporting evidence, such as:
Dated pay slips or vouchers from your employer to indicate you worked in another country after you departed the United States,

Dated bank records showing transactions to indicate you were in another country after you left the United States,

School records showing attendance at a school outside the United States to indicate you were in another country after you left the United States
, and

Dated credit card receipts, showing your name, but, the credit card number deleted, for purchases made after you left the United States to indicate you were in another country after leaving the United States.

To assist us in understanding the situation and correct your records
quickly, please include an explanation letter in English. Your
statement will not be acceptable without supporting evidence such as
noted above. You must mail legible copies or original materials where
possible. If you send original materials, you should retain a copy.
CBP cannot return original materials after processing.

We strongly urge you to keep a copy of what you send to DHS-CBP and
carry it with you the next time you come to the United States in case
the CBP Officer has any questions about your eligibility to enter.
Carrying those materials with you will also allow your record to be
corrected at the time of entry if, for some reason, the London,
Kentucky office has not yet done so.