Someone comes to us for Shabbos with a dog. May we play with the dog within an eiruv?
The dog may be attached to a leash and walked. This may be done even in a place without an eruv. The leash must be kept a tefach above the ground, and no slack should be left to hang past the hand holding the leash.
In terms of playing with the dog, one may throw it a ball to retrieve, run with it etc.. and other activities that do not involve touching it. This is according to all opinions.
Whether one may touch, pet, pick up and play with the dog is a matter of debate. Do we consider pet dogs muktzeh or are they like a toy of sorts that may be used. While many lean towards a stringent ruling on this matter, a careful reading of the sources in fact lends towards the lenient opinion. So while it would be preferable to refrain from touching, one who is lenient has who to rely on.
See Shulchan Aruch O:C 308:20, Rav Akiva Eiger ibid., Tshuvot Maharach Ohr Zarua 81-82.