I'm going to second the Hudson rec. The rail trail is a nice walk and suitable for a stroller. I think Medusa brewing still has their beer garden open (I would check before you depended on it) but they are welcoming to dogs and children, and they have food too. The main spot doesn't allow dogs inside so it would need to be a nice late morning early PM. Not sure what sleep schedule you are on. If it's something like ours (one nap 12ish-2/3) it will be difficult, but if you do a morning nap and an afternoon nap you should be fine.

Just a side note if you're looking for food for yourselves and child do not get the tacos for them, all of the varieties are too spicy for a child. I didn't think they were spicy at all, but my kid (just over a year) and wife thought otherwise. There was pain and lots of drooling, so I would probably order something from rail trail or TC landos and bring it in as they allow outside food (or did).

4-5 hrs is kind of a lot to manage with a kid and dog, I know the Shrewsbury and Northborough libraries are great to bring kids. Lots of stuff to play with along with other kids too!! But one parent would have to take the dog elsewhere while the other one stayed.

Elsworth park in Westborough is great as there is a small playground (more for toddlers-under 10 I would say) and there is a lot of open space for the pup, and a paved track good for strollers. There is also a nice playground in Northborough near the corner of 135 and 20. They have great stuff for lots of kids ages and trails nearby too for the pup.

Dean park in Shrewsbury is similar and a nice stroll too, and you could always order from Dean Park Pizza for a picnic if you wanted.

Unfortunately anything with a pup will need to be outside, which will definitely be challenging.

Those are the common things we do, as I live in Nborough have a small child and dog.