Ok, I would not assume that she is adopted because of that, given the fact that her own child was adopted (have I got that right?!) I can see that circumstances might make it more likely but there may be other explanations. 'm not familiar with the area of the country you are looking at so I consulted a map, looking at the place names you mention they are all in a relatively small area. Have you looked at Boardman families in that locality? Also, I would go a year or so either side of that date of birth for Mary / Anne it's very easy to get confused by one year, the day and month is more likely to be accurate. Given that she flipped names I would consider Ann/Anne/Mary or their own and also Annie/Anna. This is from my own experience on multiple occasions in my own family!
Also when did she die?