Did the officers have the right to search my vehicle when they found me in my wrecked vehicle which was from a DUI?

I would need more details. Police can search in the following circumstances: 1) If the police have probable cause to believe evidence of a crime or contraband exist in the vehicle. This would be the same probable cause that the police could use to get a search warrant, but a warrant is not needed to search a vehicle if the police had enough probable cause for a warrant. 2) If you are arrested while you are operating or in the vehicle, the police can search the vehicle incident to the arrest for weapons for their protection. Any contraband or evidence found in this search incident to the arrest can be used. 3) I the officer has legitimately stopped the car and has some articulable suspicion that the occupant(s) is/are armed and dangerous, the police can search for weapons and seize andy evidence or contraband found in the search 4) If the police impound a vehicle, and the Department has a policy of searching the car for purposes of taking an inventory of its contents, the police can doa n inventory search and use any evidence found as a result. In your case, if you were legitimately arrested for DUI, the police had a right to search the vehicle incident to the arrest, or if they legitimately impounded the vehicle, they could do an inventory search.

They likely had probable cause under the circumstances.

Wouldn't that be reasonable grounds.

The police are allowed to make a cursory search for weapons. If they found bad stuff in your car while doing so, it is "incident to a lawful stop," and is probably admissible in a court case. I do not believe that they are entitled to look in the trunk or in a locked glove box.

Yes, if they impounded or had the car towed.