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Your best argument to refute payment would typically be that your employer's failure to provide full-time hours constitutes a material breach of contract, thus entitling you to cancellation without repayment of relocation assistance.
"Material breach" is generally defined as a breach which deprives the other party of "substantial benefit" which he or she could have reasonably panticipated under the contract. In determining whether a material breach has occurred, courts will also consider the greater or less hardship on the party failing to perform in terminating the contract and the willful, negligent, or innocent behavior of the party failing to perform. (See, e.g. Bishop Trust Co. v. Kamokila Development Corp., (1977) 555 P. 2d 1193.)
Failing to provide full time employment, and thus full time pay, arguably amounts to deprivation of a "substantial benefit," especially if you are unable to support your family on what you are making.
A letter to your employer desribing their failure to provide full-time work as a material breach thus entitling you to cancellation without penalty would ordinarily be your best course of action. Ideally, you'd want this letter to come from a local attorney so that it will be taken most seriously. Many local attorneys can write this sort of letter for a flat fee not exceeding $400.
To locate an attorney who can help, see here: http://lawyers.findlaw.com/lawyer/practicestate/employment-law-employee/hawaii
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