Can we say "rather than to + Verb", Eg: rather than to live abroad?

Question

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"?

Answer 1

It is important that the two alternatives have the same grammatical form so, for example:

I would prefer my son to live with me rather than live abroad.

is wrong because "to live with me" is infinitive while "live abroad" is simple present. You could use either:

I would prefer my son to live with me rather than abroad.

where the alternatives "with me" and "abroad" agree or:

I would prefer my son to live with me rather than to live abroad.

where the alternative "to live with me" and "to live abroad" agree.

Where the alternatives involve different verbs, for example:

I would prefer your daughter to have accepted my apology rather than to have ignored me last night.

the verbs must agree.