I am paying maintenance and applied for / received a variation after being made redundant.
.
Your posts are hard to figure out.
Family home
You were paying for the mortgage on the family home? Were you paying the full amount? At the same time you were paying rent. Was your wife a stay at home spouse or did she contribute? During the marriage did you both contribute to the mortgage and deposit.
2 years ago you said she started to pay the mortgage, does that mean you don't pay the mortgage any more?
To decide on who gets the proceds generally is down to the contributions put in by each partner. But in divorce proceedings it can be decided differently.
Maintenance
Did you pay both spousal and child maintenance? Are you continuing to pay both
New partner
How do you know he owns his own home, does he not have a mortgage? I don't think a courts would rule that he pays rent to your wife, but he may be contributing to the house hold income (paying utilities and groceries etc) so your wife would require less maintenance, but this does not abdicate from your obligations to your children
Your needs
You say you got a variation, were you happy with that variation? If your income has again decreased then you can go for another variation. You mention redundancy, did you get a lump sum, enough to secure better accommodation? Are you working now.
Home equity
How do you think your wife could pay you the equity you think you are entitled to without getting a loan, thereby reducing her income and thereby reducing her means to support the children of the marriage. It is exceedingly difficult to get a mortgage at present, do you think a bank would entertain a loan to her on a house in both your names to pay you back the equity.
In any case you will get what is due to you when your children leave home? This will probably be based on your contributions.