What you need to remember though is that if you don't pay it then it is you, as the person with the greater income, that will be chased for the arrears and you that will be inconvenienced if the house is repossessed and your credit rating that will be destroyed.
The rule of thumb is that whoever stays in the
FMH meets all the costs as they have sole use of it.
You haven't signed up to be responsible for half of the rent each. You are both jointly and severally responsible for the full payment.
Why do you feel she should be paying towards the rent when she doesn't live there and has her own housing costs?