I've got beautiful artificial grass, in a beautiful garden filled with lots of other lovely things for wildlife, including trees, a pond, resident toads, frogs, nesting birds, a little mouse that occasionally pops his head out from under the flower pots, and last year we had tree nesting bees move in as well, so until the artificial grass haters can demonstrate that they are living a life free of environmental impact themselves alongside attracting an equally diverse range of wildlife to their own gardens, they can quite frankly naff off.
Anyway now I've got that off my chest, I came on here to say that I have two dogs, who wee and poo on the grass, and I've never had a problem. I think the trick is first to get good quality grass, but how you lay it makes a massive difference. If it's not too late, once the ground is prepared you should ask for the weed membrane to be installed first, then the sub base/aggregate on top, then a granite dust layer before levelling and adding the grass. Done like this we have zero problems with drainage and smells. All I need to do is pick up poos promptly and if they're messy ones occasionally give it a swoosh over with the watering can.
Doing it like that may be more expensive but worth exploring if you can as it will last much longer and cause you less hassle in the long run.
BTW I have successfully trained my dogs to stay off certain borders in the garden by teaching them the word off (indoors first using the sofa and a reward for off), then I picked a few days straight of nice weather where I had time off and could be out in the garden constantly supervising to translate that to the flower beds. Trying to do it for the whole lawn though sounds like an impossible task
Good luck with your new garden