Whippets should not be timid little things. They can be somewhat aloof with strangers but in a good tempered whippet that's simply down to lack of interest rather than nervousness. Timidity/nervousness can be an issue in the breed when people aren't giving appropriate consideration to temperament when breeding.
I don't have children but I've zero doubt my three whippets would be absolutely fine as family dogs. They're confident, intelligent, playful, endlessly mischievous and incredibly loving.
You do need to be realistic about the fact they're likely to have some level of prey drive, even the show bred ones. Mine (all show bred) range from moderate to absolutely ferocious. I don't find it an issue to deal with, it's just a case of being sensible where you let them off lead and really putting in the effort when it comes to recall training and impulse control. You can't train prey drive out of a dog but you can manage it can give them appropriate outlets for it.
And I worry with the inevitable prodding and poking from a toddler would upset them?
"Poking and prodding" from a toddler would upset a lot of dogs and if you have a dog with young children you need to be constantly managing interactions so neither are doing anything inappropriate with the other. This graphic is really good for explaining supervision when it comes to dogs and children. I'd also recommend reading the various articles on this list.
Whippets can also tend be absolutely vile as puppies (sounds like you got off lightly Heidi!!), very bitey and very hyper. Their night time zoomies are absolutely spectacular. More than once I've been crumpled in a heap in the floor weeping to myself because I'm desperate to go to bed but the whippet puppy is doing 100mph circuits of the room, bouncing off all the furniture and occasionally launching themselves at me to snap at my face........