DFW parking question.

Heading outta DFW to Switzerland for 11 day trip in early June. Was curious if I could offset some parking cost by leaving my car parked at the hotel I stay at the night before and taking their shuttle. It’s a noon flight and of course I’d speak to the hotel first and make sure they’d give me the green light. Has anyone ever done this? The la Quinta in euless that’s like 2 miles from airport has good reviews and offers a park n stay option for like 150$ total which is about what parking would cost alone in a shuttle lot. Any info appreciated. Thanks in advance.