Aggression problems with Great Pyrenees

[ILoveMyBerner]

I have a 10 month old Great Pyrenees and an 8 year old Bernese Mountain Dog. I got my Pyr in April when he was 10 weeks. From the start, they didn't get along very well. We had a dog that passed in Feb. and we thought maybe he was still quite upset about losing his friend. When I told my vet about a month after we got him, and he was surprised at this. He said to give it some time.

Well, its been awhile, and every once and awhile, they get into it. Nothing major, just a bark and whatever. But still. Today was the worst of it. I was in the other room and I heard them starting. I gave it a min. thinking it would blow over in a second like usuall, but it didn't. I ran out to find my G.P on top of my Berner, pinning him down on his stomach, with his teeth on his neck.
I'm not really sure if he hurt him at all, I didn't find anything on him, but he did have a hard time getting up and whined when doing so.

My daughter had chips and was running around with some in her hand. (she thinks its funny when the pup chases her) She stopped to look at something and he nipped at her. He got her shirt but any closer he would have had her arm.

I contacted Bark Busters a few days ago, before this happened, and told them about the other things he was doing, but now I'm even more at a loss! I talked to my friend who owns and breeds and shows Pyr's and she said to contact a rescue or have him put down. I don't want to give up,but I also don't want someone to get hurt in the meantime.

Any advice would be appreciated!! I'm going to try to get into the vet this week and see what he says.