Oh no, you need to find a lawyer asap. A separation agreement is action, and regardless of her action or inaction you need to protect yourself.
Don't tell her you aren't signing until a lawyer looks it over though. Just tell her you'll look it over when you have time, but you are booked rock solid for a little bit.
That's what I would do. You can protect yourself, and have her wondering what you are doing.
Me: 40 EX:37 Together 17 years Married 16 years 5 kids, 20,18,15,14,11