I was surprised at the apparent ease with which Laura could get herself engaged and then unengaged without evidently damaging her relationship with Tom. What follows are few speculations to the effect that perhaps I shouldn't have been.
Laura's mother is a dominant figure in her family. It would be natural for Laura--through the mechanisms of identification and imitation--to strive for a similar position in her intimate relationships. Mother married a man she could dominate; Laura apparently has submission to her as one criterion for the man she will live with and eventually marry.
It would be natural for Laura to be increasingly uneasy about being Mother's little girl, because becoming an autonomous adult means shedding that role. A possible recourse would be for Laura to become overtly rebellious, and thereby provoke a breakup between the two. But Laura apparently cannot bring herself to do that, which seems to be one cause of her problem.
A reason for her reluctance could be that Mother needs her relationship with Laura to continue, that it's something she lives for. It may be that Mother clings to Laura more than Laura clings back. That could explain why she disparaged Laura's engagement. By becoming engaged, Laura in effect said "I don't need you anymore," which may have been the last thing her mother wanted to hear. That Laura was able to take the step of engagement would argue that she is less dependent on her mother than she consciously realizes, that she assumes a dependent posture mainly to please her mother.
As has been discussed, another unconscious inhibition may be associated with the fear of hurting her mother by bettering her. Since her father set such a low standard, a marriage to most almost any man could be seen as improvement.
Would these two sources of unconscious inhibition be enough to provoke the eating disorders? It's a tough call without more information. Mother does seem to be the focus, and it was she who made eating a pivotal issue by being proud of her cooking. Vomiting could be seen as a "safe" rebellious act, one that doesn't challenge the relationship. Other the other hand, the eating disorders could be a way of testing a man's loyalty--"Will you accept me as I am even if that means accepting my problems?"
The sexual abuse Laura experienced does seem to place real impediments in the way of her attempts at a normal relationship with a man. Guilt as a result of the abuse could have led her to deny her sexual desires. The "training" she received while being abused could possibly have led her to also associate sexual conduct with losing control to a man. She could fear that having sex may lead her to eventually relinquish control over the relationship, with unimaginable consequences as the result.