Gut reaction is that it doesn't burn a bridge because it can always be signed back later. I would say that its only burning a bridge if its irreversible.
Plus its probably better for your kids and much as though we want to fix our marriages I think we have to have prioritise providing a safe and stable home for the kids.
Or to put an alternative slant - if she didn't and you had to move then that could be an even harder route back
Both mid 30s, 2 young kids BD 7sep14 XW moved on long ago, now living with OM1 D paperwork in progress