There are court precedents and limited exceptions where an I-130 that was approved before the death of the sponsor can still remain alive. Maybe they don't apply to you, but you should consult an attorney to figure out your situation before traveling outside the US, applying for citizenship, or doing anything else that could bring your case to the attention of USCIS. You need to find out when your I-130 was approved.
Note that in your mother's case, if she was also sponsored by your father, and her GC was approved after your father's death, she may be in the same troublesome situation as you are.