Married but filing separately? What are the disadvantages?

My wife and I have separate income, and we keep our money separate (no joint account).She sets her tax rate at her work very low. I pay the default rate. We have two kids, so each kid brings $2000 credits.

For federal tax, I'm due a return of $1200. She owes $5500. I mentioned to her I don't want to cover what she owes; we could each take one child credit. So, she should give me $3500 (what she owes minus $2000 credit). She got upset.

So, my question is, am I allowed to just file my portion of the tax as "married but file separately". What are the monetary disadvantages?