Here they say
We use rather than to give more importance to one thing when two alternatives or preferences are being compared:
He wanted to be an actor rather than a comedian.
Can we come over on Saturday rather than Friday?
Rather than usually occurs between two things which are being compared. However, we can also use it at the beginning of a sentence. When we use rather than with a verb, we use the base form or (less commonly) the -ing form of a verb:
Rather than pay the taxi fare, he walked home. (or Rather than paying the taxi fare, he walked home.)
Not: Rather than to pay …
But this site has 2 examples:
I would prefer ('d prefer) my son to live with me rather than to live abroad.
I would prefer your daughter to have accepted my apology rather than to have ignored me last night.
I would think the site is wrong.
We have to say
I would prefer ('d prefer) my son to live with me rather than live abroad.
I would prefer your daughter to have accepted my apology rather than have ignored me last night.
Can we say "rather than to + Verb"?