Even if they dont need the money, then they have to be comfortable with the arrangement. 

Our plan is to initially rent the unit to our daughter, who is highly allergic to cats.My concern is - can I cost effectively remove all traces of the cat, so that she can stay comfortably?

As far as the purchase of the properties you could do some research on owner financing and see if you and your mother would be comfortable doing a sub-2 or wrap.

If you haven't already, read through the this deal analyzing article. http://www.biggerpockets.com/renewsblog/2010/06/30...I don't know your knowledge level so if you are just getting started, take the time to read and educate yourself on the math so you can be comfortable with what you buy.  

Unless/until you feel you are 100% comfortable with all aspects of a real estate transaction and the legal issues surrounding real estate transactions, I highly recommend you use a great real estate agent and/or attorney to assist you.

My biggest annoyance is that i wanted to rent it 9/1, but don't feel comfortable doing that now without title in my name.... ah well

You could omit the exact address if that makes you more comfortable in sharing.No cost and No expectations.Thanks.

Once you are able to establish a track record, and a comfort, then you can start working more creative deal structures.  

Line up 3 notaries who are comfortable with closing wholesale transactions.5.  

You want to significantly upgrade your personal housing situation.To the extent that these conflict, you have to find the balance point that makes you the most comfortable.