I want to prevent that in the future. The solution I've come up with is to put in some kind of edging (the metal kind sold at home depot etc)and erect a wood fence touching the ground or metal edging. After that kill and reseed the yard.

Is this the best way to go about it, are there better ways to prevent incursion from neighbouring yards?

Also this is the side and back yard. The sidewalk has grass that extends past the neighbours and builds up the same problem.

Any suggestions would be appreciated :)

Violets fling their seeds to 8 or more feet away from parent plant.
Stuff blows in.
Birds drop stuff.
People and animals trek in stuff.

No way possible to have a pristine lawn.

Selective weed-killers are available to kill all weeds you've mentioned because they are broadleaved plants. Grass is a narrowleaf plant

Or start over, then remain vigilant for the few as they appear.

Well I just looked at your pic to see what specific observations could be made and realize it's not a flower bed you're trying to protect. You don't have to subscribe to the "a lawn is one type of grass with nothing else growing in it" idea unless you want to. Good luck either way!