The down payment and rehab budget would come out of my home equity line of credit and I would get a new mortgage on the rest.My father will do all the rehab and manage the property, physically.

I recommend doing some of the more higher converting lists like the high equity/absentee lists.

Since I will be moving in 2 years, I'm already planning on increasing the value of my primary residence through forced appreciation and hopefully rent it out over what I'm paying monthly for mortgage payments.I'm exploring the idea of using home equity loans and HELOCs to pay for my next house, but I'm interested in hearing what methods other military members have had success with.

I have mine in Fidelity and Vanguard no load, no fees and I can trade stocks & ETFs cheaply if I want.At Dow 26,000 I'd be dollar cost averaging out of equities honestly. 

My wife and I rolled a $60k downpayment 21 years ago into current equity around $4m today.

Because once you stabilize the property, you will have created massive equity and drastically increased the cash flow.It takes anywhere from 6 months to 24 months to stabilize a property.

Should I sell and just pay the taxes, or take out a second mortgage / get a heloc to free up the equity?

I say buy.. take advantage of thse low rates of an owner occ mortgage.. then your building equity instead of building your landlords equity. .. and since you can get roommates all the better. then if you want to buy again you have a rental in your portfolio already.. 

2) After closing if we refinance and let my wife be the only one on the mortgage and the title, how much minimum equity do we need to have in the property for conventional financing?

But I really wont have any instant equity.