Any change in a house growlithe’s living situation may cause stress, and any form of stress may manifest in a variety of negative behaviors. In short, what you’re observing is stress related to the new addition to your family, and it’s important that you treat this in order to get the hoarding behavior to stop.
Doing so may be easier said than done, however, as it will require you to exercise the utmost patience and skill with reading body language, even though what you’ll have to do is actually fairly simple. That is to say, what you need to do is set aside some time and a space for both of your pokémon to meet. And yes, they need to interact, although at first, it’s okay to have them do so at a distance. More specifically, you’ll need to set up a comfortable, relaxed environment stocked with enough toys, food, water, or comfortable bedding to keep both pokémon calm. Allow your growlithe into this space first and let her get comfortable, then introduce your rockruff. Remove one or the other and end the encounter as soon as one (or both) begin to show signs of stress.
The trick is to teach your growlithe (and your rockruff, for that matter) to stay in one place at a distance for a period of time. You may need to use positive reinforcement (perhaps by giving your growlithe treats whenever she stays or heels), but either way, you must be patient. Training out negative behaviors takes time, especially if a pokémon is responding to extreme stress (as your growlithe seems to be).