To like + object + (gerund or infinitive?)

Hello again!

Different sources give different information and I am rather confused..

to like + object + (gerund or infinitive?)

Are both gerund and infinitive possible in this construction? Is there gonna be any difference in the meaning? For instance:

[1] She likes her daughter playing the piano.

[2] She likes her daughter to play the piano.

As for me [2] sounds a bit strange.

Or:

[3] Their grandma liked her helping her about the house.

[4] Their grandma liked her to help her about the house.

Gerund is fine but what about infinitive? Macmillan and Longman say this form to like + object + infinitive is possible but it has a different meaning, other than to like + object + gerund.

If we can use both what is the difference?