The AL LLCs would then distribute the funds to the WY LLC, which would then distribute funds to us personally. 

This certainly works but have you considered creating a standalone LLC (easy) which would have a sole purpose to do a real estate investment - much easier IMO to have her get some equity or preferred equity in that simple LLC / property and get the distributions, etc. rather than setting up a mini-loan. 

Do we need to make a distribution to ourselves in order to be able to reinvest it?

Partner will take 100% of financial distributions from property until their $50,000 is recouped, then 50/50.

I  truly believe this to be what Biggerpockets was founded on, "distributing information that wasn't found elsewhere".  

(If I take the money it will be distributed to my sister and my mom)3) Do I have any legal right to stop the sale of the foreclosure and take ownership?

The rents collected would go to an LLC Account and then distribute to an private person who owns the property and would only be considered income. 

$100/door is trash.Anyone viewing the actual deal metric on the insignificant cash flow it derives is missing the forest for the trees.

Our LLC operating agreement requires Class B interests to be repurchased by the LLC at face value before any profit distributions are made.

(i) the term "Insured" also includes(A) successors to the Title of the Insured by operation of law as distinguished from purchase, including heirs, devisees, survivors, personal representatives, or next of kin; (B) successors to an Insured by dissolution, merger, consolidation, distribution, or reorganization; (C) successors to an Insured by its conversion to another kind of Entity; (D) a grantee of an Insured under a deed delivered without payment of actual valuable consideration conveying the Title(1) if the stock, shares, memberships, or other equity interests of the grantee are wholly-owned by the named Insured, (2) if the grantee wholly owns the named Insured, (3) if the grantee is wholly-owned by an affiliated Entity of the named Insured, provided the affiliated Entity and the named Insured are both wholly-owned by the same person or Entity, or(4) if the grantee is a trustee or beneficiary of a trust created by a written instrument established by the Insured named in Schedule A for estate planning purposes.