Will renting free to children avoid taxes?

[Ashley Primate]

My parents inherited 50% of my aunt's property when she passed. The house is paid off, however it is in desperate need of some repairs and maintenance. My parents would like my family to move into it after the repairs are finished (~1 year or so). However, my mom at this point, doesn't want to increase her tax burden by collecting rent. Is it legal for me to help pay for some of the repairs and remodeling and then live rent-free for a year or so? Doing this would mean she would be declaring no income right, thus not increasing her taxes?

Thanks!