Ma knows that Tom is somewhat unstable and that she is as well. This goes against her role in the family.
She is the basis for the family’s strength in the face of all their hardships. (eNotes)
Ma knows that if she becomes emotional, Tom might break down. The phrase, "then she knew", follows a description of Ma and her role in the family. She is the family's stablity:
"She seemed to know that if she swayed the family shook..."
If Ma allows herself to give in to the extremity of her emotions upon seeing Tom again, it would constitute a moment of "swaying" and may have powerful repurcussions for the family.
There is evidence for this in Tom's demeanor with his mother. He has been quite even-tempered thus far in the story, though perhaps prone to be "hard" with people. With his mother he bites his lip to keep from crying and quickly admits to his difficulties in prison.