Hi Lawgirl,
It may seem confusing, but you do have a starting point. You mentioned that your Mums original name is Woodward, then adopted to Howe. Tracing the blood line then starts with Woodward. You also mentioned that you know her father's name and location.
You need to start with the known in order to search for the unknown. Not knowing your location ( which Country you live ) . I would suggest searching the newspapers in the area of interest ( location of your blood line grandfather ) . Check the older papers for the obituaries, etc. Any type of news. Many times, the obits list the names of relatives.
If you are located in the USA. You can search some older Census records on line thru a local library that may subscribe to a paid research site. The Latter-Day-Saints, Family History Centers are another option for your research. Good Luck with your research