OP, it's hard. But it is doable. A few thoughts that jump out at me though:
With a nanny and a cleaner twice a week, I'm not sure why your house is a bit of a tip? The nanny should be keeping the DC's bedrooms clean and tidy and communal areas vaguely tidy, certainly by the end of each day. This also means that with a cleaner twice a week (assuming she's not coming for an hour at a time) there should be plenty of time for her to keep the place looking pretty good.
So first thing I'd do is really consider whether the help you are bringing in is the right help? It's hard but I'd be pretty upset if between the nanny and the cleaner they weren't keeping on top of things.
There are other things that can be outsourced - dog walking, washing/ironing, gardening etc. A cleaner will often do washing/ironing if requested or find someone else to do it. Many will collect/deliver (select times when your nanny or cleaner are at home to make it happen).
Our nanny used to prepare sufficient food for the whole family a few times a week. Can yours do that, at least a few times a week? So she'd usually do something in the slow cooker one day, and perhaps a mince-based dish one day in quantities sufficient for everyone. Ditto, our nanny did a relatively early bath time so that by the time we got home, DC were in pyjamas, place was generally tidy and they were usually watching a little tv. So we got to swan in and do the fun stuff which was cuddles and stories.
Of course, the house renovation just adds a huge extra layer. Plus, your house will always be messier/dirtier during building works so there is an element of just sucking it up. When we did our renovations we joined the local David Lloyd - we were there every Friday afternoon/evening because I just couldn't face it at home, and often on weekends too!