It's love when referring to animate objects and like with inanimate. To say you like an animate object use "мне нравится ____"
We like mom would be нам нравится мама, but it is very weak sounding. Just like in German and many other languages, the word "to love" has a stronger connotation and it is what you'd probably want to use when describing family relationships.
There's two. IIRC, нравиться means like. It's just that любить means different things depending on what it's referring to, inanimate objects or people.
To be fair, the word "love" in English also means myriad things in different contexts. People sometimes bemoan its use to describe objects, pieces of entertainment, etc. because they feel it devalues the word. "The Four Loves" from Greek have become popular among some (perhaps more academic) English-speakers as more specific descriptions for types of love between people.
Russian Day 44: Love. (This is an obscure reference to Ayreon) (And yes, I'm learning slowly)
I wrote: "We love mom." I got an approval, with the notation: "Another correct solution: We love mom."