You can buy a 2nd home with no problem as long as your debt to income is going to stay within in the guidelines, normally 50% max on a conventional loan. One thing I would caution on is the rental agreement with you mom. You dont want to put a rental dollar amount into a contract for the lender, that would be fraud, in order to get you debt to income in line. Watch your lender, or broker when it comes to this, if your debt to income is close, they may ask you for a lease signed by your mom to qualify.
If you are not currently working with a Buyer Agent and you are looking to work with a full-time real estate agent for your personal representation, please feel free to contact me.