We had lots of discussions with the dcs before we took on our new pup. (We already have an adult male lurcher, my dd is also 4, but I also have ds1, age 11 and ds2, age 9.)
We made sure they understood that it meant absolutely no toys downstairs and why (ie that swallowing a small toy could be fatal to the puppy), that they would have to accept that, as he is basically a baby, I would have to see to the pup's needs as and when it needed me, so they would have to be patient and wait their turn.
We were getting a pup in the summer holidays, so they also had to understand that it meant we wouldn't be going far, except to carry pup for socialisation purposes, so no daytrips or meals in restaurants or cafes etc.
Finally I explained that, whilst I want all three of them to be actively involved in the pup's care, I want them to allow me to do basic training and not try to continually do things like ask him to sit or lie down, when he hasn't been properly trained to do it yet. It's confusing for young pups to have lots of different people, especially young children making demands of them, using different hand signals and postures etc and personally I feel it's best for them to leave this to a parent, but be involved in lots of other ways, such as grooming, feeding, walking, playing etc then eventually positively reinforcing already learned cues, once he reaches the point of knowing what's expected of him.
We also talked about all the mayhem and mess pups can bring into the home:
Nipping,
Scratching when jumping up
Weeing and pooing
Howling at night
... and this involved lots of discussion about never putting their faces near the pup's face, no flapping or squealing and what to do if he nips or grabs their toys.
We picked up our boy just over a week ago and so-far-so-good. They all seem to be remembering our discussions and trying really hard to behave appropriately around him and help out where they can. 