The Pullman dining service has started up again so it might be worth looking at whether any of the trains fit with your travel plans. Unfortunately, they aren't doing (the fantastic) breakfasts, dinner would be quite expensive for a family of 4. You can reserve a table if you have a first class ticket, it's first come, first served for standard ticket holders.
www.gwr.com/travelling-with-us/pullman-dining
I would take a picnic rather than rely on the food trolley or first class snack boxes. There is an M&S and Sainsbury's in Paddington and lots of takeaway places, there are even more options immediately outside the station. Alternatively, you could have dinner before you leave at one of the canalside restaurants in Paddington Basin at the back of the station.
I agree with walking back across the park and combining it with a trip to the Princess of Wales Memorial Playground (it's an amazing Peter Pan themed adventure playground), feeding the tame parakeets with monkey nuts, a pedalo ride, an ice cream or splashing in the fountain.
If you feel like splashing out, rather than spending the money on first class tickets for the free biscuits, I'd go for the science afternoon tea at the Ampersand Hotel, opposite the Science Museum.
ampersandhotel.com/eat-drink/the-drawing-rooms/kids-sci-fi-tea/
You just need to go to the side gate at the ticket barriers on the tube and the staff will let you and your DC through. If they don't look clearly under 11, it might be worth taking a passport with you.