Is it possible to get a private money lender to also include the rehab cost in the total amount

HML's do it all the time.......expensive money though, 10-12% plus points.

i dont understand, your headline state 203k.. but your question is for PM or HML

@David Canecchio   I true private lender is someone you know, friends / family.  Absolutely it can be done, it's whatever you negotiate.  The lender is investing because they know you.  

I've done it a number of times with friends.

Yes a lot of lenders will do XX amount down and fund 100% of the rehab and worst case scenario is that you need to pay down payment on both the purchase and rehab amount.