Practically, the first thing I would do is arrange (along with your siblings if you have any) Power of Attorney. That is not to say that you then take over their financial matters, but it will be there when you need it.
I know that is easier said than done but I'd recommend you arrange it if you can sooner rather than later, because you won't need it until you need it, iyswim. And by then it can be too late. You want to avoid being in the situation of your dad having passed away or perhaps having to go to hospital for a few days and your mother giving her cash away to the cleaner. My dad is thousands of dollars poorer due to being old and vulnerable. By the time we found out about it, it was too late. We now have PoA, and use it simply to keep an eye on his finances. He still has control, but we'll be in a position to put a stop to anything dodgy.
I would also start looking into aged care for your mother. Again, not because you want to put her in a home next week. But because (having just been through this with Dad) aged care accommodation is very scarce (and it's an incredibly complicated process!). Now, I don't live in the UK so finding somewhere convenient and suitable maybe a piece of cake, but it may not be.
In my experience (my grandparents) dementia can progress very quickly, and can become very dangerous - we're talking burning down the kitchen kind of stuff - so having secure accommodation is really important. Like your parents, my grandfather was a bit frail, and nanna was strong as an ox but had dementia. My grandfather had a heart attack and had to go hospital so, we needed to find somewhere for nanna for short term respite care. She had dementia and was lost and confused without him (they'd bickered and fought all their lives too, but kind of needed each other). She couldn't come home to us because the environment was so unfamiliar and she'd constantly wander off and get lost and confused. Because we'd done no ground work, and hadn't had her name down anywhere we had to put her in an awful place. Just awful. I'll never forget the smell of piss.
As for their relationship, I really don't know the answer. I hope you have siblings or other family members to share the emotional load, because it may be a long road.
You could also try the elderly parents board here on MN?