"Frank does have great power over the aunt, but as I see it, the only reason why he has kept their engagement a secret is fear of disinheritance"
How does he hve great power over his aunt? Surely the whole point of the secret engagement, the main reason that it can be "excused" is that Mrs C is a snobbish unpleasant unreasonable woman and would very likely persuade her husband to disinherit Frank if he were to marry a pennniless girl like Jane. If he had power over his aunt, why would he be worred and keep it a secret from her? why would the aunt's death be teh necessary event to make it possible for him to marry Jane?
as for Jane's deciding to take the job and start her governessing career, it was a desperate decision on her part NOT IMO to force Frank's hand (if she were such a person, the tactic might well have rebounded on her since all he had to do was to go on his merry way and leave her to go to her job) but simply because she is no longer sure of F's wishing to marry her, she beleives he regrets the engagement and wants out, and she has just decided to give up on him nad get on iwht her life.