Help! Need advice please!

We are at a loss and don't know where to turn so I thought I'd ask all of you for your advice. We moved to Canada in November and are living with my mom who has a dog. You may have seen her in some of the pictures.
Before we moved we were worried that L would be scared of Petra(the dog)because she'd always been scared of dogs in England. Well we have totally the opposite problem. L is absolutely besotted with Petra and mauls her every chance she can get. She likes to hug her, poke her face, lie on her, let her lick her face, get in her basket and sleep with her and basically harass her. The dog doesn't like any of this and is not used to children.
We've tried every approach we can think of from having many conversations with L about how we need to be gentle and not bother the dog to being fairly stern, telling her she's hurting Petra to being very stern and physically removing her from the dog. Nothing works at all! We try to distract L with something else. She just goes right back to the dog as soon as she can. This is especially a problem when L is tired and she tries to use Petra to cuddle.
We really don't know what else to do. We don't believe in "time outs" and haven't had any other reason to use drastic punishments.
We don't know what else to do and don't want the poor dog to suffer or one day loose her patience. Please any advice would be really appreciated.

Sticker book

Some people have been asking about the sticker book. I found it at TK Max for £3.99 but you can get it from the website http://www.priddybooks.com/ and it is called 1000 Stickers. Older kids can use the book as is but I'm sticking them all to cardboard to use for different activities.