As far as the children are concerned the terms "custody" and "access" were replaced in the UK with "residence" and "contact" some years ago. Both parents have equal Parental Responsibility for their children and most separated parents agree living and contact arrangements between themselves. If no agreement can be reached it is open to either of them to apply to court for an order to decide the matter.
Having PR means parents can make unilateral everyday decisions, but they need to consult each other and agree about important issues such as though relating to education and health care. Obviously it is easier for children if parents can compromise and work together, but if that isn''t possible it is a case of each parent parenting to the best of their ability in their time and not interfering in the other parent''s parenting. Children are fairly adaptable and can cope with different rules in different households.
Children remaining in the former matrimonial home whilst parents take it in turns to live there isn''t uncommon in the US where it is called "birdnesting." I don''t think there is any evidence that such an arrangement works any better or worse for children of separated families than more conventional arrangements. In many cases it isn''t a tenable arrangement for the parents. Apparently there was one judge in Texas who used to order birdnesting when there were disputes about custody because it was the quickest way to put parents off joint custody and resolve the dispute!
The usual legal advice is not to move out of the former matrimonial home until arrangements for finances and children are in place. It can be difficult moving back once you have left and the danger is that if the children can''t stay with you overnight it can be difficult changing the status quo later which may leave you at a disadvantage. Are the children able to stay with you at your father''s or if you haven''t long left the former matrimonial home is there any way you can diplomatically move back?