I don't know when your ancestor's child-bearing years were, but for the sake of an example I'll assume that she was 47 in 1911 and married at 16 in 1880. In reality the window is likely to be smaller, which means that the numbers below are over-estimates. I shall also assume that you can be fairly certain that the births and deaths would have been registered in South Shields.As a side note, if anyone can think of a realistic way of identifying 3 children born to my GGM, dead before the 1911 census, I am interested to know. I am not rushing to pay for all birth certificates of children named Campbell, born in South Shields during her childbearing years - nor death certificates of Campbells dying there under the age of ten. Too many, too expensive, too depressing!
Start by estimating when the 3 children were born by looking at the gaps between the birthdates of the children who survived. This will eliminate most of the birth index entries, and you can reduce the number further by eliminating children who had the same name as an elder child who survived.
You can also eliminate children who would have been recorded on a census (because they were born before the census but died afterwards), and those who have a middle name which is obviously a surname, but doesn't mean anything to you.
Although there were 456 births in South Shields registration district in the 30 years up to the 1911 Census, there were only 118 deaths during those years of children aged 0-9 years old (anyone of 10 of more would have been recorded on at least one census). 14 of those deaths can be disregarded because the child would have been on a census, leaving just 104 deaths.
This stills sounds like a lot but when you apply the other filters you should be able to reduce the number by at least two-thirds. You'll probably end up with about 10 likely candidates, and a similar number of possibles - this is a much more manageable number, and it's likely that your knowledge of family names will guide you to the most likely candidates.
If you can provide more details (over email) this might make an interesting article for the newsletter.