What has been your personal experience with Lines of Credit being frozen? 

Credit card debt likely bad, house debt being paid off by tenants possibly good.  

If I go the conventional mortgage route and finance for 30 years I would qualify for the lowest interest rates due to my superior credit.

Have you tried private money, credit unions, smaller local lenders or portfolio lenders (they keep their own loans--don't pass on to Freddie/Fanny.)Of course you could sell the property, take a profit, and do another deal. 

I use the other guy's credit and money to buy houses.

If you can not pay for them without tenants then you could end up losing them and your credit.

Idea...Have mom list her home, sell it, put the proceeds in the bank in a joint account with you on account.The wait a few months, then purchase another property as an Investment Property with 20% down.Move mom into it, remove yourself from her account, then do a Lease Purchase, (record the lease) structuring it with you giving a credit to pay closing costs and after 12 months of having her making payments to you,  have her refi into her name.  

I would either work on my credit score to get approved for loans, or consider going back to school so I can both get a better job and use the extra loan money to buy and rehab real estate.

@Jordan Bochner I know a few local credit unions will do 3%-5% with PMI for owner occupied single families.

You can ask for concessions, but they have no obligation to accept them, and we don't know for sure if the problem is that the tenant required 60 days or if the tenant is just being difficult and their credit is bad enough that they don't care if they get evicted if it means a couple more months of a roof over their head.