Mothers like to watch their children eat / eating and play / playing.

The problem I've come across is whether it's possible to use the infinitive in this sentence? It seems to me that yes, it's possible, but I need an explanation of this use. Normally grammar books (I needn't give a special title, just almost all of them) say that one should use an ing-form in situations like that, when the accent is on the continuity of an action (because mothers enjoy watching the process of eating, playing etc. Or one can't use an infinitive here?

Eat is OK and suggests the whole process/meal.

Thank you, Tdol. But I just can't undestand why one should want to suggest the whole process here, I can't think of a context (for the sentence in question) where the whole process would be important, usually mothers just enjoy looking at their children. I just can't feel this difference. :-?

And if I say "I like to see her dance" will it mean only "I like to see how she dances from beginning to the end"?

***NOT A TEACHER***

This might help.