Kendal may be nice, but if you are moving to Barrow for work you are looking at a commute of around 1 hour each way. The A590 - the only road in and out of the Barrow area - is often subject to roadworks and awful delays which can be very stressful.
As for schools in Barrow, Chetwynde was a private school with a good reputation. Due to costs, numbers were falling and this year it has become a "free school" and is over-subscribed. Chetwynde caters for kindergarten up to sixth form.
The main secondary school in Barrow is an amalgamation of several schools and is Furness Academy. The building looks wonderful but sadly for the children of Barrow has been bit of a disaster. The head was suspended last year and his temporary successor has just resigned. It is in special measures.
Those who mention Walney, the secondary school there is also in special measures. Unfortunately the third secondary school and probably best regarded, St Bernards, has also had difficulties. The only way is up!
I had a colleague who thought Barrow Island was a wonderful rural location conjuring up images of palm trees. Do google Egerton Court to give yourself a more accurate picture.
Ulverston Victoria High School has an excellent reputation as does Dowdales Secondary in Dalton. Children travel from all around the area to attend these often over-subscribed schools, so don't go rushing out of the area.
I am from Ulverston and live in one of the local villages. I am not a huge fan of the town, I find the atmosphere rather odd. For example they are trying to Keep Ulverston Special (?) at the moment opposing a Sainsburys.
Barrow does have a number of rough areas, it is a working class town, but also beautiful places like the Abbey. There are nice areas - Abbey Road, Croslands Park etc which are pricier and very handy for Chetwynde and various primary schools. I find the people friendly.
Newbarns Primary school in Barrow has a good reputation. It is a large primary school with around 500 pupils.
Don't disregard village primary schools such as Pennington, Urswick, Lindal etc which are pretty good as well.
The local villages between Ulverston and Barrow such as Scales, Gleaston and Urswick have nice properties. It is around 10 minutes travel to Ulverston and 15/20 minutes to Barrow from these locations.
Hope this isn't information overload and anyone is quite free to disagree with me!