The options are:
1 Both stay at home, with visiting or resident carers.
2 Your dad goes into a care or nursing home. Your mum stays where she is.
3 They go into a home together.
1 could be relatively cheap or extremely expensive, depending on level of care needed. If they're not self funding the cheaper end of these, with 2 - 4 care visits a day, is what the LA usually prefers to try first. But if care needs are too high they can go straight for residential.
2 will cost more than brief care visits but probably less than live-in carers, and be cheaper than 3. If the care place is near his home your mum can visit daily if she wants, and in a good home there won't really be limits on how much of the day she spends there (although she'll need to either bring in her own food or pay to eat there).
3 can be them being in the same room and both paying for full care even though your mum doesn't need it yet, or some places have a staged series of care levels so your dad could be in the full care section and your mum in an independent or supported living flat on the same site.
I agree with PP that the first step is a social services care assessment. This will help decide how much care is needed and narrow down the options, and confirm whether they're self funding or not.
With Parkinson's and regular falls it's likely that visiting carers won't be enough - he can't be left lying on the floor until the next scheduled visit. So you're likely to be headed for one of the residential options - soon, if not immediately. It's therefore worth starting to look at what's available