Depends on the children, depends on the dog. It's a gamble and it's more of a gamble than if you didn't have young children because the range of behaviour you can accept from the dog is likely to be smaller than if children were not present.
e.g. puppy nipping is something adults can understand but young children may struggle with. Keeping precious items out of reach is something adults tend to do better tha small children who may be upset to find their favourite toy chewed up.
Only you know your children and know yourself. Puppies do really require pretty much full on supervision for a while. Are you able to provide that and provide the right level of attention to your children, for instance? Again, the exact amounts required from everyone will depend on your children, yourself and the specific dog you end up with. Some puppies nap more than others, some take to being left to sleep better than others, some toilet train much quicker than others etc. Expect to be giving full-on attention to the dog (when awake) for the first 6 months, ish.
Cockers and Cavaliers have quite different temperaments and a mix could end up being more cocker/caver than poo so do make sure you understand all 3 breeds and can live with whatever the mix throws out. Good and bad.
If you wfh for the majority of the week, that suggests times when you don't. And there will (presumably) be children activities the dog is not welcome for. Think about what you do with a young dog. You cannot leave them alone at such as age and you may struggle to find a professional dog care setting that takes such a young puppy on. Or maybe you both work away on different days? Something to think about. In fact, thinking through everyday scenarios is also useful: if the children are sick can you leave them home while you walk the dog or will the dog have to go without walks, or will you make sure you or your parnmer can cover at home? When the dog gets older and requires longer walks, are your children old enough to 'keep up' for 30-60mins of walking or will one adult walk and one stay back? Do you go on holidays and what kinds of holidays? If you end up with a dog that doesn't like crowds does that impact your life in a way you won't accept?
Not trying to put you off. I just think it's worth thinking through everything you do in a day, plus any realistic changes to your routine (holidays, you being sick, visitors, play dates, parties etc) and how you will accomodate or adapt for the dog AND young children.