First time Doodle owner and 3 yr old yorkie is being mean. Help!!

[Trixie]

Hi all, new here and looking forward to many years of joy with our new golden doodle.    First, some history.   Female yorkie is 3, we lost our 13 year old lab in the fall.   Lab was awesome with yorkie and they were best buddies.  Slept together and hung out all day long in the same space.
Now we have a beautiful female golden doodle.  Just got her yesterday, and the yorkie is snipping at her.   I make the yorkie submit and lay flat each time she snarls/nips, but I see the puppy is afraid of her.  The puppy will try to come back to play at a later time, and I don't want to have the new puppy cower from the yorkie.
I want to make sure we do all the correct things to aid the relationship along in the right direction.
Any suggestions?

[Allyson, Peri & Taquito]

Trixie....don't worry about the yorkie (what's his name??) being protective over you. That will subside in the future. And Taquito still does that every once in a while if he is on my lap and is tired and Peri comes up with her big 'ole paw to swat him. It is just doggy nature, so don't sweat it. I am so happy they are romping around - that will just continue and their relationship will blossom before your eyes =)
Thanks for the update.

[Trixie]

Trixie is the doodles name. Gracie is the yorkie.

[Trixie]

wanted to post update. as you can see by the new pix of the girls kissing, they are getting along great!!! We just gave Trixie her summer cut so she can swim, and she still looks cute. Different but cute. We all miss her long hair....

[Allyson, Peri & Taquito]

That is wonderful news!!! I thought they would become great friends :)