Because the dog comes TO home not comes FROM home

In this case 집에서 would mean "comes from home" as in going somewhere else.

That means "the dog goes home" - you want to use 오다 instead of 가다 to mean "to come"

It's 옵니다 (오다 infinitive) , "to come", not 입니다.

~에 is a locative particle - here it means "to," literally "the dog comes to the house"