If I acquire a second house subsequently, rehab it, rent it out (past the "seasoning" period), and try to refi it to get some money out to repeat the process, will I run into issues with the mortgage on my first home when the lenders see that I do not have income from a job to pay for the first mortgage, thus will refuse refinance of the 2nd house?

I have a lengthy Legal Opinion, from my seasoned Legal Team regarding this matter.

Strategy would be to buy the property using the Wrap and then turn around and refi when the seasoning allows for it.

A few points: Per the Fannie may guidelines for the “delayed financing exception”, you can borrow up to 75% LTV, OR your initial purchase price (this can include closing costs), whichever is LOWERLots of people have had success with including rehab costs on their HUD / closing statements, so that the second part of the above guideline isn't the limiting factor, enabling a BRRRR-type strategy without having to wait the full 6 month seasoning period.

Other than that, find the person or company that has what you're looking for whether it's something like 1-4 unit, no income verification, 25% down, score down to 650 on a property that's stabilized with short seasoning or just a long term funding solution on a single family after the renovation is complete.  

Weird story: I am in a Facebook group and talked connected with a lady who is losing her home in Wood County, Ohio.

Especially as a newbie.Only well seasoned investors should ever do this. 

I just wasn't sure on what the more seasoned investors thought about where to tap into funds for the 25% down and if there were any advantages or disadvantages to one or the other. 

The seasoning period doesn't have to do with how you purchased the property.

There are ways to get someone in there for the off season.