Is 'ist' necessary?
I may be tripping myself up and overthinking, but:
Ein kleiner Hund ist mit der Frau spielen.
Die Frau spielt mit einem kleinen Hund.
Now, my interpretation is that the first one means 'a small dog is playing with the woman.' but that the second sentence could mean either 'the woman plays with a small dog' OR 'the woman is playing with the small dog.'
So there is no need for 'ist' in the second sentence unless you specifically want to say 'is playing' rather than 'plays'? Which would sound more natural in real spoken German?