I live about 20 mins away. I just told my mom and caregiver to follow him about 20 paces back as he keeps saying I don't need you guys. They live in a pretty calm and secure neighborhood designed for 55+. It's small with sidewalks etc so he was safe except for the risk of falling. he went to the wrong house, but still insisted he did not need help form caregiver or my mom. I got there and got him in my car and took him to lunch but he's just hung up on not wanting the hired caregiver there. he thinks he and my mom can handle everything. I wrote about this a few days ago. my fear is the wandering and the fact that my mom goes into panic mode. I read that keeping them busy is a way to deter the wandering, but he does not want to engage in anything!
Your mom must now put secure locks on all doors and up high too to keep your dad in the house or it my be time to have him placed in memory care.
And while mom is getting things figured out, please have her talk to your dads doctor about putting him on some medication for his agitation.
Memory care often have a fenced in courtyard he can walk around without getting lost.
Start looking for a memory care facility , Dad is too uncooperative to live at home.