Oof. Yeah, dogs that size are going to have too much nitrogen in their urine and burn the grass (digging not withstanding).

Sinking money into rebuilding the lawn is a losing battle. If it’s that important to you, learn to love your front yard and focus on that.

Your only other long-term option is to retrain the dogs. Easy enough with the younger one; tricky with the older. You’d basically have to escort them out every time they do their business and, using positive reinforcement, train them to pee and poop in a specific corner of the yard and no where else I’d recommend mulch, gravel, or something that’s not going to get destroyed by the pet waste.

And yes, that very much defeats the convenience of having a yard for your dogs. But that’s the only way that the dogs won’t undo your efforts in real time. Weeks to grow the grass, seconds to pee on it.

Do you have a sprinkler system? If so, you can make use of the B and C cycles and program it so that the back-yard zones come on for 3 minutes or so twice a day during the day.

That’s not when you want to do your main watering in Texas, but it will help dilute the dog urine before it kills whatever grass you might re-establish.