What about the lady’s insurance company? She should have “uninsured motorist” coverage. At worst, she would have to pay her deductible. Has she filed a claim with her own insurance company?
Everybody seems to think the "uninsured motorist” coverage covers damage to your car by a driver w/o insurance. It does not cover damage to your car. It covers medical expenses for injuries to non-relative passengers resulting from an accident caused by an "uninsured motorist”. The damage to your car from such an accident is covered under your collision coverage and is subject to your deductible. If you have a high deductible to keep premium cost down, it comes out of your pocket. You can attempt to recover through legal action but you'll have to "squeeze blood out of a stone".
If the driver is an illegal, he's probably in the wind by know and will be impossible to find. You could try "small claims court" against the construction company, it might be your only option.
Regards,
GtG
PS Your insurance company will tell you that they will try to collect from the UM and you will be reimbursed for the deductible in the same percentage as they recover. Don't hold out much hope as they don't try all that hard. IC to UM "pay up", UM to IC "no", IC to UM "pay up or else", UM to IC "go ahead, I ain't got squat", IC to UM "OK, have a nice day". IC writes off loss as a "business expense", you get screwed. (from personal experience)