What a terrific story! I think you have done a masterful job of combining character creation with some sophisticated humor while wrapping it all up in a good mystery story line. I enjoyed the entire story, but I know that you are not looking for accolades without some constructive criticism, so here are a few observations.
In your e-mail last Saturday, you said it was a work in progress, with the end product being 6 small chapters. What you submitted thus far is apparently half of the book as it contains 3 chapters, but ... it seems to me that it has reached a resolution at the end of the 3rd chapter. The missing babies have been found, alive and well, and Esmeralda apparently was also found, alive and well. If there are three more chapters, I can't wait to see what else takes place.
There are a lot of words in the text that I had to look up in my dictionary; orb, mandibles, spinneret, lintel, cloyed, and even Arachnid. Perhaps that's merely testimony to the inadequacy of my own vocabulary, (and a chosen avoidance of becoming familiar with spiders!) but I wonder if your targeted audience will have a similar problem. Just an observation for you to consider.
In Part 1, you start by saying that Esmeralda was late this morning, suggesting that was the first time it had happened, yet on page 3, in the italicized part, Newt is thinking she's been gone a couple of days. Similarly, Arial says (page 2) it was the day before yesterday when she had bundled up her brood, but on page 3, Newt asked her why it took her a week to start looking for the children.
Still in Part 1, I didn't see the connection when (bottom of page 2) Newt was remembering how birds sometimes stared into the eyes of a snake too long. I understand that you are conveying the hypnotic effect that the eyes may impose on a would-be victim, but it seemed to me that the spider was there to get help, not size up another meal.
On page 3, 5th line from the bottom, "Arial's eyes ..." Shouldn't the word "detective" be "detective's?" (knit-picking :-)
On page 4, where Newt is listing the key points of his investigation, I thought Arial lost her children right after the unknown perp ripped a whole in the web; not after she ate the damselfly. Also, you repeat that Esmeralda has been gone a long time when it initially was only since she was running late the morning the story begins. These same comments apply to the second summation on page 12.
On page 6, middle paragraph, Newt pounced on the millipede and "clutched with all his feet." How many feet does a lizard have? Or did you intend that to somehow mean all of the millipede's feet?
In Part 2, page 2, when Xavier was pleading his case (4th line from bottom of the page,) shouldn't you insert "to be" between "was" and "my?" Also, wouldn't you want to add a comma between "well" and "go missing" on page 10, last line of 3rd paragraph? And on page 11, middle paragraph, shouldn't there be an apostrophe in the italicized word, "its" (middle line 5th paragraph?)
I have two comments about the encounter with the snake (page 11.) Your text states that "Thousands of small Newtons cavorted in the snake's iris." First, I've never wanted to get close enough to a snake to find out for myself, but do snake's eyes even have an iris? If they do, would the word "cavorted" be the best descriptor? To me, cavorted suggests movement, action. I would think this would be more a refracted image of an intended victim, frozen, motionless.
Take a moment to reread the paragraph beginning with "Newt rocketed up ..." and see if you don't think there are too many consecutive sentences that begin with "the."
In Part 3, the spider diva refers to Newt as MR. Newt after earlier on they had invited each other to be less formal. Should this be either Newton (without using Mr.) or Mr. Lizard? (or am I knit-picking again?)
I love the dialogue throughout the entire story, and I love the characters you created; the "snooty" Arial, the despicable dung beetle, the "gang" of hornets led by Tony the Sting, etc. I could visualize the movement of your characters, particularly Tony's ZZZZZZZing-ing arrivals and departures. As stated before, you managed to include just enough wry humor - such as item #5 on his list of important things gleaned from his conversations with other characters - to keep it entertaining. I am reminded of listening to the old detective stories on the radio, and I surmise that is the effect you are trying to achieve. If so, in my opinion, you succeeded.