Should I scrap my plants? (Mite related)

[AprilMayJune]

OK, I am an idiot (and a very newbie gardener) and even though in hindsight I've probably had them for weeks, I just now realized as I'm preparing to plant outside, that my tomatoes and peppers have mites. Weirdly, the plants actually seem to be doing OK considering (the peppers, especially, look really healthy and have been growing very well except for the occasional spot where you can see the mite webbing/very minor leaf spots.)

I am pregnant and have a small child, so I don't/won't use harsh pesticides, so basically I'm left with soap solution and maybe a couple other "safe" alternatives if I feel up to it, but I'd need to do more research. I did apply a ton of soap solution already but I fear it's too little too late. I have no idea if I can manage to beat them back at this point, because, again, I didn't even realize what the problem was for a loooong time. This is only my second season of serious gardening, but still. Embarrassing.

My question -- do I need to to throw in the towel on these plants? Is there even a point to pressing onward with infested plants, or should I call it quits and buy some new plants from the store (even though it will kill me to have to do it?) I seem to recall that one of my pepper plants got mites last year (though further into the season,) and it still grew and produced and was OK (I'm not looking to grow the biggest/highest producing plants in the universe here as we're just a small family so I could live with somewhat stunted plants, just not half-dead ones.)

Gardening. Such a learning experience. Sigh!