How can I get rid of wild garlic/onions for good?

They are tough little dudes. Probably any solution will affect your daisies. Digging them out (pulling still often leaves the bulb in the ground) is the best way but very time consuming. Herbicide applied after the greenery shows is the other option.

You may not like this, but in 50+ years of gardening, I have found this is the only way that works. Alliums are persistent. Bulblets tiny as a pin head lurk sprouting off the parent bulb and as seeds in what appear to be immature flower heads.

If the stem blade is a thin hair and the ground is moist, you may pull it out gently, making sure there is a single bulb attached.

If the stem is anything thicker, carefully dig it up making sure to obtain ALL the miniscule bulblets. DO NOT SHAKE OFF excess soil; you'll just be re-seeding unseen bulblets. If you wish, carefully screen excess soil into a container and observe container until positive no new shoots emerge. REPEAT as needed until bed is clear. Be prepared to repeat over several seasons. When removing flower heads, immediately place into plastic trash bag and discard.

I have never been able to create a compost heap hot enough to kill off allium or tomatoes! (All of the above applies equally to dandelions, except that leaving a tendril of a fine root is the below the soil culprit.)

U can dig out the daisies then sort thru the dirt ti get the bulbs out then replant the daisies. If u use a herbicide, and want to protect the daisies u can use a paint brush to apply the herbicide to the growth that has sprouted.

Daisies will self seed so normally the following season u will have double the number of plants, When I didn't deadhead mine crowded out and killed the other flowers. I don't know if they would kill off the wild garlic or not but its a thought.

regardless, getting rid of the wild garlic will not be easy. best of luck.