My Mom lives with my family and is on limited social security. If she pay us rent and utilities, does that complicate her getting Medicaid?

Do a share of costs and not a rental agreement. A rental agreement makes the money she pays towards her share of costs income to you. She is paying her living expenses and that is different than renting.

No, it won’t complicate Medicaid as they expect her to have normal living expenses. It is very good idea to have a rental agreement or contract stating what she’s paying for though just in case any issues arise with Medicaid.