Lark Lane is a short 15 minute drive from the port, it has a very good selection of restaurants, Marantos is very good, any restaurant you Email will tell you about disabled access and bathrooms.
http://marantoslarklane.co.uk
One of the best Italians is Crust
https://www.crustliverpool.co.uk
The Woolton restaurant has toilets on the same floor, the Bold Street one is in the basement so may not be suitable.