Only once you are much bigger and your LLC has collateral or a track record that you can document to the bank will you be likely to get a non-recourse loan. 

I would like to take out single a line of credit with the 3 units as collateral.

The LOC is already collateralized by something else and guaranteed by you personally.  

Like ANY investment, things can go wrong--BUT--you have a written contract AND good collateral if underwritten properly.

Call and talk to lenders, follow up on some of these posts with referrals to creative lenders with more flexible criteria, look into commercial loans that look at the property as collateral and have lower borrowing requirements.

Keep in mind the 2008 downturn was pretty darn severe and the laws that were in place unfortunately prevented a lot of mortgage loans to be re-worked as they were part of large collateralized mortgage packages sold to investors via Wall Street. 

However, I don't have the money for the down payment, and I don't have the collateral to get a loan for the remaining amount (of $150,000).

You would need to file a Form 1099 and issue that to your mother to report the interest paid (assuming the $50k loan is not collateralized.

The collateral of the mortgage would involve international law.

Like a secured loan with my 401k as collateral?