If you are looking to buy a new house, and want to keep your current home as a rental property, on a Conventional loan you need to show the lender who is making the loan on your new home some things that you would not if you were selling your current home instead of renting it. You need to show 6 months "cash reserves" after the down payment and closing costs on the new house, and you need a 70% loan-to-value (LTV) on your current home, as evidenced by an appraisal.
If you meet both of these requirements and have a lot of equity and cash reserves, you can count the rental income on your current house to offset the mortgage, which will help you qualify for the new mortgage. Otherwise, you will have to qualify for the new mortgage carrying "all" the debt on the current mortgage and using no rental income to offset the debt, and usually most people cannot qualify for two mortgages at the same time.
And if you do meet the cash reserves and the 70% LTV requirements outlined above, the banking industry will only count 75% of the gross rent on your current home (as evidenced by a lease) to offset the mortgage. They take away 25% to account for vacancies, expenses and maintenance. So if you have a $3,400 a month mortgage, and can show a $4,000 a month lease, they will only count 75% of that $4,000 a month lease (or $3,000) against the old mortgage. In this case, $4,000 gross rent, with $3,000 net rent (after a 25% deduction on the $4000 gross rent) would leave a $400 a month shortfall and would be counted against you as a debt in your debt ratios.
When people learn of the above, they end up realizing that in many cases they need to sell their current property, because they do not have sufficient equity to meet the requirement and they cannot qualify carrying two mortgages at the same time without counting rent to help cover the old mortgage.
If you are taking out an FHA loan for your new purchase, the rules are the same except you only need a 75% Loan-To-Value on the current home, as evidenced by a recent appraisal. Either way, buying a new home without selling yours, and trying to rent your current home, has become much more difficult.
Maybe you can move out of the house, rent your unit, start to collect the rent from your mother on the books, and show a 1 year history of collecting the rents. Then if you can show a tax return that shows that you have a one-year history of collecting rents, the equity requirement goes away. Then you could use the rental history to offset the mortgage, and buy what you want. Of course, that means you're going to have to go be a renter somewhere else for a year. Good luck.