SQL Server 2008 - Two FULL backups in one day
Would be there a problem with POINT IN TIME recovery? Does his backup broke our chain?


No, Full Backup has no affect on transaction log backup chain. You would still be able to restore full backup and all log backups in sequence. So let us say you have following


Full backup 1 taken by you
Log backup 1
log backup 2
Vendor Full backup 1
Log backup 3
Log backup 4
Vendor Full backup 2
Log backup 5
In case of disaster you would be able to restore Full backup 1 and then log backups 1,2,3,4,5 in sequence. 


Having said that you can ask vendor to take copy_only full backups just to be on safer side and simplify things

Hope this is what you are asking.