I think.....
Although, Joe bought Home Farm it was with his Trust Money. It seems that Kim (Tate) probably managed to gain a large fortune during the years she was absent and went to prison.
I think Frank Tate was pretty much penniless when he died; swindled out of Home Farm by the King family which is why Zoe blew it up as she left for New Zealand with young Joe and baby Jean.
Kim had a son (possibly Frank's or Dave Glover's) who Frank accepted as his - James Francis Tate. Now, James would be Joe's Uncle.....and any 'Tate Estate' would be his before Joe's.
I think it's going to get a bit convoluted but I am sure all that ^^^^ will come to play somewhere.