If you mention at court that your dad is putting money towards the mortgage you are weakening your case against your husband, as it will look and be as if you have access to other financial resources outside of the marital assets, and therefore not needing as much financial help from your husband as you claim to do. You said you put the deposit down of your first house, but believe me, since you are married, it doesn't matter who did: The assets belong to both of you and same goes for the debts.
It is a minefield. But this is something I wish someone had told me BEFORE we went to court over the minutiae of things: Before a judge could rule, you have to be to court three times. You are expected to negotiate to get to an agreement in between court appearances (via solicitor, mediators, yourselves), but he or you can always ignore the other party's requests/demands/offers/negotiating efforts until a judge offers a ruling.
He can stop paying the mortgage and any other bills if he wishes to. And he can't be forced to pay until there is an order made by court (in a final hearing in the worst case). If you are lucky, you may get reimbursed for the expenses if that order is favourable to you but it could take between months and years for you to get the court to rule. And in the mean time the bill is running high.
Hence the need to keep the negotiating channels open, find a mediator, try to sort the stuff out of court. Everybody suggests using solicitors but very few know that in plain terms, a solicitor charges an average of £3 a minute, a barrister way more than that. A day in court with a solicitor may easily cost more than £1000, a barrister for a day... I have no idea but mine was about £3000.
So my advice, better to save the money to put down a deposit on another house.
Talking about savings, one of the things my solicitor said which was actually pretty good advice was to take advantage of the good times (while he was still paying mortgage, private school, etc) and get myself in a better financial position before getting the courts involved. Because once the courts were involved, the rug was, as she predicted, pulled under my feet. Fortunately by then I was in a better position to deal with things, the house prices had gone down a bit which made things more affordable and I had increased my working hours/salary a bit.