The White Hart isn't far from your hotel, not quite en route to the stadium but it seems to have made a comeback since they started doing food. Not been in there recently myself but I'm pretty sure you'll have no trouble with having kids.
"Remember last time they were here, the Huddersfield Giants, they lost to a Luke Walsh drop goal. He's only scored four drop goals in his St Helens career has Luke Walsh and each and every one of them have been scored by Luke Walsh"
I would suggest you grab a taxi and ask for Stockton Heath.....cost about £5 in a taxi. Only a mile or so away from town centre. Maybe end up back in the town centre later on about 12ish.