Looking into the northern Caucasian connection with Indo-European, I found descriptions of similar wedding traditions among the Circassians and Chechens (NW and NE Caucasus groups, resp.). The bride is held ransom by her side of the family (no specific item is taken, e.g. a shoe or knife), and the groom's side must pay to get her out of her house. A variant is the bride's side putting up crude roadblocks and not allowing her to pass through until the groom's side pays the ransom. (I recall reading about this roadblock variant in the Polish, too.) As in the IE groups, this is all on the playful / prankster side of things, not an official bride price. So this tradition must go back to the common cultural ancestor of the northern Caucasians and Indo-Europeans. End of update.
I recently watched a YouTube video about how crazy Punjabi weddings are, one example being the ransoming of the groom's shoes. The bride's side steals his shoes, and the groom's side must get them back by paying the ransom requested by the shoe-nappers. He can't very well leave without his shoes, so paying the ransom is required for the wedding to be completed. As far as I could tell, the shoe-nappers are female, and the ransom-payers are male. The key thing is that it is a form of bride price.
During an unrelated YouTube search for knife dances, I learned that Persians have a similar wedding ritual. Only with them, the women on the bride's side steal the knife used for cutting the wedding cake, and the men on the groom's side must pay the ransom to recover it.
That suggested a common origin among Indo-Iranians, hence perhaps as well among Indo-Europeans.
Sure enough, the Armenians have a similar ritual, where the only difference is that it's the bride's shoe that gets stolen. But it is still stolen and held for ransom by the women on the bride's side, and the men on the groom's side must pay the ransom to retrieve it.
The Armenian version is also found in all three major branches of Slavic peoples -- Poles (Western), Russians and Ukrainians (Eastern), and Serbs (Southern). Probably in the other members of each branch as well; I stopped counting once I found a member from each branch.
Among the Balts, Lithuanians have a custom of the wedding table being occupied by a fake wedding party, who require a ransom to give the table over to the real bride and groom. The groom's side (best man) carries out the negotiations with the impostors, though I couldn't find out whether the money goes to the bride's side or to the guests in general.
In Germany and Austria, the bride herself is kidnapped and whisked away to a local pub where she and her bridesmaids and friends drink until the groom finds her, after searching the area. He pays the entire tab for what they have drunk, and she is allowed to return and complete the ceremony.
Something like the German/Austrian kidnapping is found among the Romanians.
The tradition seems weaker in Southern Europe. I couldn't easily find something like this in Italy or Spain. In Portugal, the bride's shoe is passed around to the guests like a collection plate, and they leave money inside it. This does not involve kidnapping or paying a ransom (i.e., making it seem like the wedding cannot conclude until the money is paid). It also does not distinguish between the bride's side and the groom's side -- it's more about the guests giving money to the couple.
It is a bit stronger in Greece, where (at least in Epirus) the bride complains that her shoes are too loose and must be padded with money by the groom, who does so until the bride's side agrees that it's enough. It involves back-and-forth haggling as in other Eastern places.
I also could not find much in the way of ransoming, let alone of shoes, in the Celtic parts of NW Europe or in Scandinavia.
Overall, though, the phenomenon seems pretty widespread, often down to the particular item that's stolen -- shoes. What this means in the greater context of Indo-European culture, I don't know off the top of my head. "We leave this matter as a topic for future research." Still, it's neat to see a ritual being shared among people who trace their genetic and cultural heritage back so far.
Rituals tend to be conservative -- you're supposed to follow the script and not change it. And for rituals that are more common, you get more practice carrying out the script. Common rituals are less prone to error since they're something that "everybody knows" how to do. For rare rituals, you might genuinely forget how they're done and introduce mutations or scrap them altogether. It's hard to think of a more common and frequent communal ritual than weddings, so they ought to be a good place to look for conserved performance forms among people who have common ancestry going way back.