If there is no self-employment, then you would need to look at an IRA based plan for putting that savings to work in real estate.When you invest an IRA or 401k in real estate, it is entirely for the benefit of the plan.  

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You could roll those old 401k dollars into a self directed IRA, but as @Dmitriy Fomichenko said, if you are flipping within said IRA you could be subject to UBIT.  

Can one purchase a rental property with a child (4 year old) and use some of the earned income to fund a kid Roth IRA?

I am referencing the book "Leverage your IRA" by M.Allen, 2nd eddition page 159 on Property Management: "The rules allow you to perform ministerial service for your IRA.

Will this work with a Traditional / Roth IRA? 

I have a self directed IRA, but my situation is a little different from yours.

I told him he is better off buying a rental property or opening a SEP IRA for the deduction since the big truck he was looking at was $45,000.It's crazy how some people justify spending $45k on a shiny object and think it's an investment when it's an expense.

CustodiansList of Large Self Directed IRA Custodians (Over $2 Billion under custody):Equity Trust Company (acquired Sterling Trust Company)First Trust Company of OnagaIRA Services Trust CompanyKingdom Trust CompanyMillennium Trust CompanyPensco Trust Company (acquired Lincoln Trust Company)Provident Trust GroupTrust Company of AmericaList of Mid-sized Self Directed IRA Custodians ($500 Million – $2 Billion)Advanta IRA (TPA)GoldStar Trust CompanyMidland IRA (TPA)New Direction IRA (TPA)Next Generation Trust Services (TPA)NuView IRA (TPA)Self Directed IRA Services, Inc.

Next, to the extent you are eligible, max out roth IRAs, traditional IRAs, and SEP IRAs as they offer a great deal of asset protection as long as you don't play games.