Is it possible to breed pets in the sims 2?

Yes, you can breed pets in the sims 2. See http://sims.wikia.com/wiki/Breeding#The_Sims_2:_Pets

In The Sims 2: Pets, a pet house is required. This allows the player to have the selected Sim command a pet to try to have puppies/kittens with another pet. The Sim must have a good relationship with the selected pet to successfully command it. Additionally, the two pets must also have a good relationship with one another. If successful, the two pets will go into a pet house and WooHoo. If the female pet becomes pregnant, the player will hear the same music that plays when a Sim conceives.

If you do want to control the pets yourself, you can use the cheat boolProp controlPets on after opening the cheat console with control-shift-C.