The private screening is a VERY good point.
The person walking thru the metal detector CANNOT touch the unit as they pass they. Mom could walk but preferred to 'hold onto something' for stability. THAT caused major issues with the security process.
Also I would NOT wait until arrival to ask for help. Put it in your reservation so the airline can PLAN for support. Skycaps and the wheelchair pushers are minimally trained for these type of supportive jobs. The airline may have a Handicapped Manager (or liason) at larger cities.. something you NEED to put into the paperwork sooner rather than wait.
Just something more to think about with your situation.