I've always been a little confused about Molly and whether she's a rabbit or a Marina-type of dog.  The Arthur Wiki lists her as a rabbit, but if you look at her character design, her nose and ears are identical to Marina's.  This leads me to conclude that she's really a dog.  James, by contrast, has the more common rabbit nose design that we see in Buster, Ladonna, etc. 

We know that her mother is a dog, and her father is a rabbit.  This leads to the conclusion that:

1.  Molly is a dog, and is her mother's biological daughter.  James is a rabbit, and is his father's biological son.  Their parents got married after they were born from previous marriages/partners of the same animal race.  OR
2.  In the Arthur universe, it's possible for animals of different species to interbreed.  In this case, Molly and James are really dog/rabbit hybrids.  This could explain why Molly's snout is much shorter than her mother's, and James's ears are more similar to Marina's than Buster/Ladonna's (assuming this isn't just due to him being a young child).