Hi Stuang, a mortgage deed is a legal document and therefore is not as simple as some people think to change/have names taken off.
Basically it ALL comes down to finances and status. The mortgage was originally set up and agreed with the lender offering certain specific criteria. Your existing lender will want to know that your partner has a secure job and a sufficient income to replace your ex on the mortgage. They will also want to know about his outgoings eg other mortgages, loans, child maintenance, maintenance etc etc. Basically, they will want to know his nett monthly spending worth before considering replacing your ex with your new partner. If the figures stand up you will need to employ a solicitor for the change of name on the mortgage deed.
As for your partner coming off of his mortgage, the exact same criteria will apply. Remember, if his wife has not got a new partner with a supportive income AND if there are children involved, her solicitor is very unlikely to agree to him coming off of that mortgage deed.
This is certainly possible to sort out but it is not going to be straightforward unless you are very fortunate in having a new partner of some financial worth or his ex has found the same. Very good luck to you for the future.