Often they will accept a "gift letter" confirming the gift is outright and not an undisclosed loan.

You will have to pay gift tax.  

All contracts, options, or other devices not based upon a substantial consideration, or that are otherwise employed to permit an unlicensed person to sell, lease, or let real estate, the beneficial title to which has not, in good faith, passed to such party for a substantial consideration, are hereby declared void and ineffective in all cases, suits, or proceedings had or taken under this chapter; however, this section shall not apply to irrevocable gifts, to unconditional contracts to purchase, or to options based upon a substantial consideration actually paid and not subject to any agreements to return or right of return reserved.

Talk to your accountant about gifting.

Could we use cash from a home equity loan on the property in MI to provide a down payment for a new place in HI, and if that could be used as a gift to us and allow us to use my husband's VA loan? 

Gift them a copy of BiggerPockets' book First to a Million, written specifically for Gen Z.https://store.biggerpockets.co...

You can't get gift from your sister for investment.

A 3-year lease is no gift to landlords as it prevents increase in rents for three years, results in more early terminations than a one-year term, and if you get a bad tenant - 3 years is a lifetime. 

Possibly, by having my mom 'gift' part of the down payment, but it would have to come from the money she'd make on the sale..

If she felt gifts were more important than rent, my guess is you did not adequately screen here application, or else your standards are very low.