I work as team leader in a team of 6 (2 very senior devs, 1 senior dev, 1 medium level dev, 1 junior dev and 1 senior graphic designer). Our client has his own internal team of 5 (1 architect, 2 senior devs and 2 junior devs).

The performance and the skills of the internal team are extremely low (commits that don’t compile, even tags, merges that break/remove working functionalities and that reach untested the production, nonsense question, month to develop simple changes, etc.) and we are always fixing their poor job. For example: 

 - we fixed dozen and dozen bugs opened in the last year and a half and that were assigned to the internal team, spending less than 30 minutes on each (even in part of the project we have never worked on before); 
 - a project was assigned to the internal team and was estimated 3 months: after 6 months they admit they were unable to complete it, so client assigned it to us. In 6 month they did less than 10% of the required work. In a month and a half we closed this project
 - We had to pass more than a week to fix svn mess they did

From the beginning of this years, the client more or less bypass his own team and assigns everything directly to us (in fact our team will soon grow of at least 4 devs). They didn’t take it well and are trying to sabotage us: we need them to contact other suppliers because for their internal policy 2 suppliers cannot speak directly without client mediation and they literally take weeks to simply forward an email; when we need clarifications on code they developed, they are elusive and don’t provide any useful explanation, they didn't give us resources or privileges that we required in order to complete our tasks, etc.

Client is well aware of the situation but he seems he wants to do nothing to solve. Someone that pass through a similar situation has some advice on how to solve this problem?