My husband is also a veteran with no outstanding mortgages.If we purchased a home that we would AIRBNB/VRBO part of the year, they (our children) would be interested in the ownership of it as well. 

I had to fight and fight and fight to keep them from wanting to demo my house.Some of these places don't really have a big tenant base, so that can be challenging too.Good luck....and best wishes.

The last thing I want as a new investor is to fight 'analysis paralysis' because I'm not confident in the numbers I've come up with. 

Right now buyers are pretty much fighting for homes when they hit the market, resulting in rising prices.

Just make it clear that the cost of purchasing from you, will be less than the cost of fighting it out in court with you. 

How does one fight this to ensure that it doesn't affect your score?

In our local market, deals are still available on the MLS, but you absolutely have to fight your hardest to get them, as well as being ready to purchase at a moments notice.

I have a rental property in Louisiana, and that property is newer with outstanding tenants and cash flows nicely.

I'm currently considering an investment purchase that has a very low (3-4%) cash ROI, but is in an outstanding area with lots of potential for appreciation.  

@Jake DotsonI hear you on the market value but its still worth fighting against.