Amira le goy

Question

Hello again, In 2 weeks is my sister in law's Chabbath Kala. My in-laws live in a area with no erouv and they plan on having all the Chabbat seoudot at shul. My problem is we have a 1 year old baby (he can't walk yet). 1. Would it be moutar to have a goy push the stroller Friday night back to the house, Chabbat morning to shul and back after the meal? 2. If it is permitted, can we put the babies stuff (food, dippers, change of cloths...) in the stroller, or do we have to bring them before chabbat to the shul? Thank you in advance. Chabbat Chalom.