Yep, respect is the name of the game with dogs, but especially small dogs because it's so easy for us to ignore their boundaries and dismiss their polite "please stop" or "I don't like this" signals. That's a big reason why small dogs have a reputation for being 'nasty' - they learn they have to resort to snarling and snapping because nobody listens when they're polite.
Make sure the dog has a kid-free zone, whether it's a bed or playpen or a room, that he is always able to retreat to if he's feeling overwhelmed and where the kids are never allowed to follow or bother him in. They can ask him politely if he wants to come interact with them (like calling his name), but if he stays put, that means they have to respect that he's not in the mood to play and needs space. No more pressure.
Always supervise when he and kids are together, and encourage appropriate interaction, like mutual toy play (tossing, gentle tugging, etc), gentle petting, etc. Do not allow any play where the dog is encouraged to play with body parts, roughhousing, or the kids grabbing and picking him up, or otherwise physically manipulating him. The former can lead to a dog who doesn't realize that mouthy play with human skin is a no-no, and the latter can make a dog uncomfortable and insecure, and more likely to growl or snap because toddlers don't see the subtle signs that it's going too far. Play should be pretty calm and loose - if things get too high-energy, make sure everyone takes a break. When dogs are amped up, they're more likely to use their teeth inappropriately or jump on people - jumping might not be a huge problem with a chi in most cases, but with a toddler that could put excited puppy teeth at face level and that's generally a bad idea, even if it's playful, because baby puppies don't realize human skin is more delicate than dog skin typically is.
Make sure you're also not manhandling or physically manipulating the puppy more than necessary. It's a lot of fun to scoop up puppies and cuddle and love on them, especially when they're tiny, but this can actually be pretty frightening and overwhelming. Imagine a giant you've only known for a week or two grabbing at you and picking you up unexpectedly, not even giving you the ability to move away because they're holding your feet off the ground. Absolutely love and cuddle, but try to 'ask' the dog to come to you with your body language and voice, and respect when puppy doesn't seem to want to approach or be picked up. Sit on the floor to cuddle, so puppy can safely climb in and out of your lap if he wants.
Read up on dog body language, so you can better pick up on those really subtle cues that he might be uncomfortable or uncertain, like tense facial muscles, lip-licks, looking away - even talk to your kids about it and learn together how to better understand your new family member. Lili Chin does wonderful illustrations about dog body language and behavior that I bet kids would respond well to, like
this one here. Allowing a dog to have agency about when and how it interacts with you empowers them to feel safe and confident, makes them WANT to engage with you more, and helps avoid that "small dog syndrome" people talk about where he feels he has to resort to nasty snarls and snapping to get some space. If he has that with you, he'll have more patience and flexibility if the kids push his boundaries sometimes.
