The fact that Team A uses Kanban and Team B uses Scrum is probably incidental to the situation. Fundamentally, the two teams have a different attitude towards quality of their work and its impact on their customers. Besides impacting Team A's performance, they may also be impacting their external customers, which management may not even be aware of.
The long term solution is to show Team B the impact of their shoddiness. Perhaps the Support organization can show some analysis of support tickets for the company and see if there is indeed impact to customers for Team B's work. Perhaps there is market release data for products that both teams work on to show that Team A's products are getting to market more often, thus positively impacting company revenues. There certainly needs to be some management intervention based on this evidence to motivate Team B to improve.
However, in the short run, some other steps might also work.
One way to do so would of course be for Team A to have a frank conversation with Team B to explain their situation and see if there is anything they can do to help get the video player release on time. If they can somehow get that message across, that would help Team A. They could even enlist an external coach/ trainer to help them with this task.
Second, given Team B's past performance, Team A can forecast when realistically they will actually get a bug-free version of the player, and incorporate that in their own release plans. So, specific tasks and features that integrate with the player can be done earlier in the release cycle, so that integration efforts can begin and all bugs reported by Team A can be fixed by the Team B. Perhaps a couple of cycles of this testing can be pre-planned and incorporated in Team A's release plan. Separately, all other features of Team A's release can continue (the ones that don't depend on the player integration) and finish in parallel to the testing, debugging and the final release of the video-player and its integration to Team A's product. This way, they can continue to make releases as per their plan while incorporating the rework of Team B in their plan. The picture below hopefully helps illustrate my point :)
If needed, the two teams might have to do multiple iterations.
Easier said than done, of course! Clearly, Team B has issues relating to team management, team dynamics, individual motivation, etc. that makes them continue to function the way they do. Unless these are addressed, including perhaps rebuilding the team with some fresh blood and ideas, this will continue to drain company resources, revenue and profits - as also overall employee morale.
HTH. Good luck!
