Duality

Most mutations appear to be one-off affairs (and thus not genetic in nature and not transmittable through flower pollen), but I have found patches of daisies that tend to generate mutant flowers (never one that always generates mutant daisies, mind you, otherwise my garden would contain significantly more abominations against nature than it already does).

The tendency-to-grow-mutant-daisies plants likely have messed-up DNA (which means that the mutation can probably be transmitted via the flowers' pollen), but that's not really a point against picking the mutant daisies from them - the non-mutant daisies on that plant will spread the mutation equally well (because all the flowers on a given daisy plant are grown from the same DNA and transmit the same DNA with their pollen) and there're always more non-mutant daisies than mutant ones on any plant I've found to date. It has a negligible effect on mutation propagation, in other words. Or, in a few less other words,

Also, there's like a zillion daisy plants I've found mutant daisies attached to around my neighbourhood, so obviously the mutations are doing pretty well for themselves without my mad-scientist interference. I fear for the fate of the world if I start bioengineering daisies.

I know there's glow-in-the-dark flowers somewheres...

 Well, if its visible, then that means its a phenotype, right? Do forgive my lack of science knowledge, haven't cracked into a science textbook in ages now despite having on on the dresser behind me. If it is a part of its biology enough to be observed, then surely it's a part of its DNA to be on a repeatable basis to be passed on in a predictable pattern, right? All natural mutation can be coaxed, right?

You know they've made glow-in-the-dark bunnies, right? Glowing flowers are old news.

I'm fairly certain you're entirely right (biology is too applied of a science for my tastes, so I'm not really the most reliable of expositors when it comes to phenotypes), but the not-visibly-mutant flowers on the mutant-flower-forming plants should pass on the mutant DNA just as well as the visibly-mutant flowers do, because all the flowers on the (mutant) plant pass on the same (mutant) DNA, even if the flowers aren't all visibly mutant.

There's usually like ten not-visibly-mutant flowers for every visibly-mutant flower on a given mutant-flower-forming plant (don't quote me on this I made up that number on the spot), so picking only the visibly mutant flower still leaves ten times the number of not-visibly-mutant-but-still-containing-mutant-DNA flowers still alive to pass on the mutant DNA and corrupt the source code of biology one daisy plant at a time.