Here's a somewhat analogous case which you could cite in support of your eligibility:
VOLUNTARY LEAVING, Health, Reasonable alternatives, Involuntary leaving
CITE AS: Haynes v Flint Painting, Stripping and Derusting, Genesee Circuit Court, No. 94-32420-AE (August 16, 1995).
Docket No. B93-13254-128491
CIRCUIT COURT HOLDING: "When an individual is caught between a rock (leaving her employment) and a hard place (risking her health), the decision to act one way rather than the other is not a voluntary leaving."
FACTS: Claimant worked for the employer for two years before learning she had breast cancer. The claimant's job involved heavy lifting and extensive manual labor. Claimant requested another position because of the strain on her health. The employer informed claimant that no alternative position was available. The employer informed the claimant could return to work after completing therapy. The claimant did not return to work and filed a claim for unemployment benefits.
DECISION: The claimant is not disqualified from receiving benefits under Section 29(1)(a).
RATIONALE: In light of the totality of circumstances, claimant acted reasonably when she chose to leave rather than endanger her health. She was not in the position of exercising any reasonable alternatives. Laya v Cebar Construction, 101 Mich App 26 (1980). The court found this matter distinguishable from Watson v Murdock's Food and Wet Goods, 148 Mich App 802 (1986), because the claimant approached the employer and requested alternative work, unlike the claimant in Watson who intended to leave her employment due to complications with her pregnancy. The claimant in the present matter left work after learning that alternative work would not be available. The claimant was "forced from a position that her health would not allow her to perform, and employment which her employer did not take steps to continue."
Just substitute "family" for "health" as in "the claimant acted reasonably when she chose to leave rather than endanger her FAMILY."
I suggest you print a copy of the Haynes decision summary and bring it to your hearing and give it to the ALJ.