If you've cleaned up all the poop that was in your yard, then bring some home from the park/walk and place it where you want her to go in the yard. Since she used the yard initially, at least you know she WILL use it. Walk with her in the the yard (don't just let her out), especially first thing in the morning and after she eats her meals. Don't play with her and don't distract her with toys or lots of chatter.......just stay calm and occasionally repeat a command such as 'do your business' or 'go tinkle' (the commands for my dog). When she does go, give lots of praise and then play with her if you want.
If she refuses to go, take her back in the house and repeat in 30 minutes. Use the same commands wherever you take her and she'll soon be comfortable enough to 'do her business' anywhere.
Question: have you noticed if she prefers a certain surface to go on? Some dogs prefer either dirt, grass, mulch, or hard surfaces. If you've seen this preference in her, then try to supply the same in your yard.

If you completely stop taking her to the park for a day or two, the dog absolutely will poo if it is eating and if it is healthy. Period.

It's like when someone says a dog will not eat a particular kibble brand. Again, a healthy dog will not starve itself to death by refusing to eat.

Sometimes tough love really is required. It is in the best interest of the dog.