I wouldn't tell her she's free to join you. That almost sounds like you're inviting her (i.e. Pursuing). Some of the vets could speak better on that than I can, but that's my feel.
I'm doing in-house separation too, and I sleep in the master, and she sleeps in our daughter's room. It was easy because that's been the sleeping arrangement for the most part over the past year or so anyways (and was probably detrimental to our marriage).
I find that the key to living under the same roof is to be mindful of her space. If you share the same master bath, give her the privacy and make sure you leave the room when she's changing/showering. If you're changing/showering, and she comes in, then leave that alone (i.e. don't call her out for invading your privacy). But try to time those when she's not there or during times you know she's elsewhere in the house.
Here are some of the things I'm doing, and it may apply to your situation as well:
Don't follow her around the house. Don't initiate conversations with her unless necessary. Let her say "good night" and "good bye" to you first.
When she's watching TV, don't join her on the couch. Don't ask what she's watching.
When she's spending time with the kids in one part of the house, don't "jump in" to what they're doing. Allow her (or your children) to invite you in.
M: 15 years BD: 6/25/14 EA/PA: starts 5/14/14 11/30/14 - A ends 5/15/15 - D is finalized. 11/28/15 - Start of new LTR with a wonderful woman (and still going strong)!