It is 'sort of' possible in Premiere Pro. I just experimented in Premiere to check.
Try this: put the first card into your Premiere Pro sequence on V1 and place and 'scale' it to the size and position it will first appear at (see image). Do the same for the second card but put it on V2 in your sequence.
Once both cards are positioned - right click the first card on V1 in your sequence and select 'nest'. Do the same for the second card on V2.
Now apply the 'twirl' effect to both nested clips in your main sequence. I found I needed to set the 'twirl radius' in the effects control for each twirl quite high (57). Now animate the twirl angle for both nested layers and they will twirl around each other to a centre point.
That's the basics and should get you going. Play around with the twirl radius - maybe have a slightly different radius for each nest. Playing with the 'twirl center' in the effects controls may also yield something interesting.
The two images with this post show the above.
