If getting a new dual antenna, you typically need to match it to the laptop model as it will need to fit in the same space with the same folds, etc...
For instance, on a Dell XPS 15 9520 you need part number N4HD5. Need to know the specific laptop to typically find this information.
Looking at a pic of the old WiFi card and comparing against what the card is supposed to look like, it is clear that some of the metal grounding/shielding came off the card's connector. Here is what the card is supposed to look like:
What you need is something like this (typically called a "parts puller"), but designed/sized for small electronics (this image is for one sized for car/truck bearings and will apply upwards of 7tons of force):
You can try using a metal workers bench vice, but my guess is that will still have too much slop in the clamping distances to let you push/pull only the shield that came off the old WiFi card and not clamp down on the male end of that connector and bend it out of shape.
You might be better off trying to use knife sharpening stones/diamond plate/sandpaper to hand sand through a small section of that outer shield (and not the inner shield) so you can then use picks to pry it off. With how thin that material is and that it is probably copper, it will get cut through very quickly even with just 400-600 grit sandpaper. You should only need to sand through a single small section (not the entire piece) to let you then use the metal picks to get a better purchase on that shield and spin it/pry it up and get something else to be able to get a grip on it to pull it off.
Another thought would be to put it in the freezer for 30-45 minutes to get it nice and cold and then bring it out and try and warm up just that outer shield (a quick pass over a candle or heatgun). The heat would "expand" the outer metal shield compared to the inner shield, helping to separate the parts a little (this needs to be quick as the heat will get conducted from that outer shield to the inner part and that will also start expanding).
That all said, if you don't already own those kinds of tools, it would probably be cheaper to just buy a replacement antenna, but investing in the tools would be worth it over time since there are other things you can fix.