Hiya CG,
I wonder if this is the point at which your dad will start to realise that he can't continue without something happening. I was wondering if you could perhaps help engineer things so they happen gradually without your dad realising. By this I mean rather than day care could your mum start by going for residential care, say, 4 days a week and then home with your dad for 3 days. The hope being that over time your dad realises that your mum is in the right place in the home and that rather than taking her home, he can visit every day if he likes but has additional staff there to help carry the load.
Funding/payment could be for full time care with your dad merely taking your mum for a few days, which is acceptable. It means however that on a bad day you're not waiting to get respite arranged. Your dad can take your mum back immediately. Same goes if he is unwell. Although these plans can be put in place, we found with my mother that we had lots of plans, take her on holiday, take her home for Christmas Day, take her to the garden centre for a cup of tea and slice of cake...very quickly we found none of them materialised because the routine of the home was what she needed and the people who were familiar to her were her new extended family and it was us who had to fit in with her and not the other way round. I know your mum has been on respite before but this would be different because her room is there all the time. Respite is one off periods of time that don't leave much time for your mum to settle. This would be a permanent 'part time' arrangement.
At least this way when your mum is away, she is cared for and your dad is completely released from the caring role such that he is not constrained by day care times etc. doesn't mean he won't continue to worry though!
I reckon that very quickly the number of days at home will reduce naturally or things will escalate at the home such that they perhaps have to take DoLs safeguarding action, which is beyond the control of your dad.
Lots of arguments that can be used to help your dad. Winter is approaching. Bad weather. Not nice to have to get mum up and dressed and out to day care every day. He would still be her carer but with other people around to give immediate support. You feel that you might be more able to visit your mum too if there were more people around.
Anyway, just my thoughts...
Fiona