When she feels there is less tension on both sides of the gate, she should get a family member (or a friend) to take the shelter dog out to a large, fenced-in area while she takes the resident dog and turn them loose. The dogs will not feel trapped and will investigate each other before starting a roudy game of tag.
The two humans should not stand together while they supervise this play. By standing 30 or 40 feet apart, they will be able to break up any potentially aggressive moves or vocalizations by the owner cheerfully calling the resident dog while the other person calls the shelter dog. Be sure to praise and reward the animals for coming when called.
Go easy on this segment of introduction. A short play period is best at first and both dogs should be rewarded at the end so the whole experience will be a pleasant memory. Each outing afterwards can be a few minutes longer period.
Now I need to mention growling during play. Not all growling is aggressive. My schnauzers all sound like they want to kill and eat the playmate. Fortunately I know these vocalizations are normal play. So if the resident dog and shelter dog growl when they are playing, look for the play-bow (down in front, up in rear). Check the tail, is it up and wagging? Watch for the dominant stare, if both are staring directly at each other, call them to you immediately. You might call "Fido, come. Do you want a treat?" Both dogs need to be called at the same time.
If the dogs are looking at each other from the corner of their eyes with heads slightly averted, that means playtime. Let them have their fun.
Obedience training both dogs and asserting your leadership by making sure you are the first one out the door or up the stairs, and the one who gives permission for them to follow you is necessary. Be sure you eat first before the animal. Individual playtime can also teach leadership: "Sit, wait," (then you throw the ball), "Fetch," "Come," "Give." Good dog!