Teddy's mother and father are a typical, almost cliché (or should we say archetypal?), mother-father duo. The mother is a bit timid when it comes to all things "nature," as we see when she's afraid to have Rikki-tikki sleep with Teddy (15). She even faints after the incident with Nagaina on the veranda (107).
In the same light, the father is your typical father, knowledgeable and practical. He understands the nature of mongooses, which is why he doesn't worry about Rikki-tikki sleeping with Teddy. He's prone to action, as we see when he joins Rikki-tikki in fighting two of the three serpents. He also knows that Teddy should stand perfectly still when confronted with Nagaina (89).
But no matter their differences, both characters come to accept Rikki-tikki as part of their family in the end.
But is this practical, comforting dad nothing but an oppressive colonizer? Well, he's got the firepower for it. Twice in the story, the father uses weapons to kill native creatures: first, he uses a stick to attack Karait, and then he pumps a slug into Nag via shotgun.
If we view these native creatures as representative of the native Indian population (see our "Character Analysis" of Nag and Nagaina for more), then we can clearly see the father as a colonizer who uses violence and superior technology to keep the native population in line.