I''m not sure if either of you can actually register a claim if you haven''t lived there. Although you would both be able to claim on each others assets if there is no Clean Break, I don''t think this goes as far as gaining land registry rights on properties you haven''t lived in. And any claim on assets can only be done through the courts if you don''t agree.
However, I''d like to make an observation here and you will no doubt respond angrily. I read a lot of your posts and you criticise your ex in bucketfuls. Today, because he does not want to give you more money he is the ''lowest of the low''. He is unwilling to look after your son (that is a joint ''your'' and not ''his'' as you often state) but you don''t seem prepared to consider the reasons why. Perhaps he is finding money tight and needs to work , perhaps he has thrown himself into work post divorce or perhaps simply he doesn''t want to do you any favours when you clearly don''t rate him. I am sure there will be many injustices on your part too; the problem here is that you are getting so entrenched in your respective positions that fairly normal things like not wanting to give more money to your ex are being rated alongside the crime of the century. You made similar judgements on his character earlier this week when he failed to respond to your phone calls, although it turned out it wasn''t a contact day and he would have had no idea why you were ringing him.
It''s hard when you have a child and things are unresolved, but the best idea is to cut off all but essential contact, have a care plan that you both agree on regardless of the levels of contact, and above all get your finances resolved once and for all.