If you list them as accompanying, she has to at least have permission from their father to take them to Canada. If they do not stay in Canada for at least total 730 days in the next 5 years after getting their PR, they will lose it again. On the other hand, if your wife lives in Canada for a solid 3 years, then applies for citizenship, she can apply for the children too if they are under 18 so if they spent at least a couple of months in Canada during those first 3 years, they do not otherwise have to meet residency requirements for citizenship if she does.
If you list them as non-accompanying, she can sponsor them later but be aware that she can only sponsor them under the federal system until age 22 unless they are full time students. Possibly she could sponsor them under a provincial program for longer, depends on where you live.
Thats a quote from Leon 1 of the more knowledgeable person on the forum please take a look at the bolded part your wife NEED permission to take the child to Canada