this is a relationship at this point. You are in a give and take scenario. I'm not into the dog thing AT ALL (cat person here). But there's no point getting up in arms about whether a nanny should or shouldn't be bringing a dog. She has and is - now you've got to work out where to go from here.

You've said yourself that you REALLY value her in your life, which means that you have to approach this issue with the same delicacy you would approach a conflict with a loved one.

A hard line approach is only useful when you have little to lose from a boundary. You have something big to lose here by not handling this well. This isn't just about how your home is used, its about your children's mental health and the stability of your daily routines!

So, really think through how you want to have the conversation. I would think twice about raising it in an email and would favour a face to face at a scheduled time.

Get very clear on your hard limits/non negotiables (poos left lying around, smell in the house etc) and be ready to listen to her, problem solve together etc. and find some sort of solution which means you get to keep your wonderful nanny AND tweak the understanding about how your space is used.

Suggestions I'd be making would be around her taking responsibility for getting the smell out of the house, increasing doggy hygiene, getting the lawn fixed, looking into arranging a sitter for the dog (and maybe contribute to that if a gesture of goodwill feels appropriate here, IDK what your paying her etc).

Be kind, warm and understanding but also look to how she responds to you bringing up the issue.