Hi Roy and welcome to the forum. You'll have some fun with that outfit, totally suited to an adult and two kids.
I don't know Cleethorpes but have had a quick look... do you mean the slip near the pier and/or the one a little further down from the pier they call the Brighton slipway?
Looked at the charts too and it seems at lowest tides it can dry out to a mile or more sand/mud so you need to get the tides right or it will be a long pull back on the transom wheels.
Personally for family leisure use I don't like launching direct into the sea as if the wind picks up and there are breakers when you return it can be very dangerous. Far prefer a slip into a more sheltered estuary or harbour.
But there may be Cleethorpes regulars on here who have better local advice.
BTW seem to be a lot of rules...
And this gives an idea of the sort of terrain you'll have to cross if you get the tides wrong!