Video doorbell pro 2 and 2 doorbells

I have two doorbells connected to a digital chime. I replace one with Video Doorbell Pro 2 and that works great, and the digital chime works too. The problem is that the other old doorbell now doesn't properly ring the digial chime: 1st button push results in nothing, second push sounds one chime followed by some static from the speaker, a third sounds a double chime (the way it is supposed to sound).