Repeating (or not) "to" in a sentence involving infinitives set in parallel

I googled it but I couldn't find the answer... maybe I didn't seek it in the proper way.

My question is if "to" must be repeated in sentences such as the following ones:

• In the past, women used to do the housework and to take care of children.

• The aim of this meeting is to control their progress and to discuss the new working plan.

If I had to bet, I would omit the second to... But I am not sure about it.

In both cases, the second to can be omitted; to introduces an infinitive phrase, and that infinitive phrase can include a compound verb. Hence, for example, To Live and Die in L.A. (the title of a movie from the 1980s), where in L.A. modifies live and die, and to introduces the whole thing.

In your second example, it's also fine to include the to. In essence, both of these are fine:

The aim of this meeting is {to {control their progress and discuss the new working plan}}.
The aim of this meeting is {{to control their progress} and {to discuss the new working plan}.

(In the latter case, it might be better to say "The aims of this meeting are […]", but I think it's fine as-is.)

In your first example, however, I find it pretty awkward to include the to, because used to is an idiom, pronounced /ˈjuːstə/ (with a /s/ sound, not a /z/ like used), and I hardly feel that it contains the word to anymore; so the second to doesn't sound like a repetition of the already-occurring word to, but rather like a first occurrence of the word to. Granted, it doesn't sound anywhere near as bad as something like "In the past, women would do the housework and *to take care of children" (which is completely ungrammatical); but I would still find it surprising in modern American writing.