Following an accident, it's your legal right to have your car repaired anywhere of your choice.
If you contact your insurance company they may try to get the repairs done at the lowest possible price without caring as much about quality of the repair as you do.
You do not need to use your insurance company's favoured establishment, so look after your car and not the insurance company's profits!
Also, you do not need two estimates, and if your chosen bodyshop is a CUI member and offers the ColorGarant life-time paint warranty, then they guarantee the quality of all work undertaken. What's more, for added value, the paint guarantee stays with the car for up to 30 years.