I have mobility issues and am a lone parent to two autistic children, so we have to pick our holidays carefully!
My advice is:
If you go by plane book a taxi from your house to airport departures, and from your destination airport to the hotel. They will lift all baggage for you and you won't have to negotiate car parks etc. Same for the return.
Book special assistance for airports if going by plane (although how helpful they are is... variable. To put it politely!!)
For a hotel ensure they are aware of your needs in advance. Do they have kids clubs and can your children do this? Otherwise you will have no respite. Some hotels have a nanny service. You would do well to find a hotel with direct pool access from your room so you and your mum could rest on the terrace while kids swim? Or perhaps if that costs too much be better off booking a villa/ ground floor apartment with direct pool access, so that you do not have to go out if you don't want to.
I have found it far easier to get ferries than flights e.g. to St Malo or Santander. Drive on, take just an overnight bag to the cabin (worth booking decent ones) then drive to the destination. Much less hassle than airports.
That said, we have done various flights within Europe, and my children are quite a bit younger than yours. I have found the airport process exhausting but that is partly due to my own health plus their autism and them getting overwhelmed and yours are older so will be much easier to manage in that environment, so I really do not think it should be too hard for you. You just need to ensure the accommodation is accessible and practical for your mum and her being able to enjoy time with you all: so there are places to go where you can all go together once there.
Paphos itself is reasonably easy to navigate, although very touristy. There are parts of Cyprus that are nicer. You can drive there very easily so renting a car is a good idea, if that's where you decide to go.