It is very hard to say if it is the same woman. But the hairstyle is similar. The beach/lea photo is better than the the sitting photo and both are not great.
My comment on the woman is that they are of Filipino race - not necessarily nationality. And yes the woman next to Obama is also of Filipino heritage.
As for photoshop - it is hard to tell with these supposedly old photos that have been scanned, resized, cropped, etc. They are small and poor to start with.
IF both women are the same person, the ANNE/USA at the Nachmannopfs and the girl close beside the kenyan in the Dock image, then one might be forgiven for making the assumption that what we are looking at is the woman who is referred to as 'the wife in the Philippines from whom he is separated...'
That she may have been living at the birth announcement address, listed as Ann S Obama...and subsequently shows up in Seattle, as ANNA OBAMA, for whom Mary baby-sat in January, 1961. And she's obviously NOT Stanley Ann Dunham.