I'm very sorry to hear that you have lost your mum so recently. Losing a parent is very hard. It forces you to realise that life is short and to face your own and your Dad's mortality.
However, I think this is clouding your better judgement here, so I am on team DH. I'm afraid I would not agree to another mortgage at age 55. You've managed to become mortgage free, which presumably is now making life much more comfortable financially, even though your salaries are good. You need to stay that way and build up your savings and pensions much further.
I understand why you feel the need to move. We lost my Dad just over a year ago and the result is that my now widowed elderly mother lives alone, a three hour drive away from us. She also has her own health issues.
Moving house has to make financial sense too. What you are proposing doesn't. It sounds as though you could afford to buy a different house outright near to your Dad. Surely that would make more sense financially if you feel you really must move.
Sorry, but I do feel that your DH is right to put the brakes on this. Mortgage free status adds to your financial security and isn't something to be given up lightly, especially at 55. That is the age when many people are looking to be done with mortgages, not to take another one on. He is probably also happy as he is, even though he has indicated that he may consider a move if no mortgage was involved. Again, that seems sensible to me.
Look for a cheaper house that will need no mortgage. If that doesn't work out then maybe take on a short term rental near to your Dad so that you can take your time to get a feel for how things look likely to go. Don't just plunge straight into an expensive house purchase. It could end up being an expensive mistake.