I wouldn't have expexcted it to be aggressive as such, but some whippies will snap when frightened, though as you think it is playful I am sure that it what it is. Lots of sighthounds do this when excited, I don't think you will be able to stop it tbh, just closely supervise as your children are young. Eventually as you come to know him well you will realize he is unliikely to ever catch them 'accidently'.
Lots of whippets love to fetch and can be taught an excellent recall, but it will take lots of patience. Mine is ball obsessed now, it is a brilliant way to channel the chasing instinct and will help to give you some control. It is also the game my children most often play with him, arm a child with two large dog teddies, to keep small fingers away from big teeth, child throws one teddy, dog brings back, child throws other teddy, picks up first teddy, repeat until bedtime
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My children also play piggy in the middle with him, chucking a dog toy between each other, while he tries to get it, but they have been raised around dogs and are very philosophical about being splatted by a flying whippy.
I am also happy for my 6yo to play tug with him, but not my 3yo (purely because he would just keep pulling her over).
Most play with young children and young dogs is quite boisterious, I think the key is supervision and maybe prevention if you/your children don't feel comfortable with it.
By the age of somewhere between 18mo and 2 and 1/2, he will turn into a totally different dog, calm, chilled, mostly sleeping, super easy going.
Puppy and adult whippets are so incredibly different temperament wise, it is easy to wonder if they are different breeds altogether
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