"Home" doesn't need a preposition. Perhaps because it's a "relative" location, ie. your home is not my home, but other locations like "the city centre (of Barcelona)" are definite places. The same rule applies to "abroad". I often hear students say "go to abroad", which is a basic mistake.

'We got home' is the correct form. 'Home' doesn't need the word 'to'. For example you'd say: We ran home/ We walked home/ We drove home.

"We got home" is correct. "Home" shows the place so includes "to". On the other hand, "house" shows the building.

"We got home." (The other choice is incorrect.)

we got home