How would you split up 5 weeks between England / Scotland / Ireland?

I'll be traveling with my wife and our 4 year old in April/May. We're not looking to have a whirlwind holiday and see as much as possible but rather see enough of some choice places in England, Scotland, and Ireland. We have 5 weeks and planning to rent a car. Our very uninformed, first draft idea was 10-14 days in Southern England, 10-14 days in Northern England / Scotland, 7-10 days in Ireland. How much time would you recommend spending in each location?

Thanks!