Do you know what pests you’re dealing with are? You can plant companion flowers that repel certain bugs, as well as plant trap crops (like radishes) to attract certain bugs away from your main crop.
Other flowers will attract predators to the bugs you don’t want.
As for neem - are you using a cold press concentrate or a premixed bottle? Premix bottles aren’t very effective from what I’ve read, and as long as pets and children stay away from the wet cold press neem spray, there should be little to no worry about contact.
Just be sure to spray a small section with any new solutions you try so you know if your plants will like it or not - better to lose a few plants than your entire garden.