I agree with you.
"There are children liking swimming" is ungrammatical I think, and sounds non-English (this is not a sentence a native speaker of English would produce I don't think).
"The children are liking swimming better this year" is perfectly normal and correct.
Here the present progressive means that the children are starting to like swimming better and that the time in question is this year; that is the children do not habitually like swimming so much as they do this year (and yes there are children who for a while hate swimming; I can give an example of a child who hated swimming but came to love it as an adult; she hated it because in the 60's the people who taught her swimming tended to throw her into the deep end when she did not learn or behave and she always just sank to the bottom and waited for them to fetch her . . . Ah most of you all did not go to school or take swimming in the 60's and things have changed a bit I guess).
Anyway . . .
a sentence that means about the same thing, and that might be used more frequently, is:
"The children are enjoying swimming more this year.:"
You're welcome, Nick, Jr. I doubt I explained usage that well here. I'll try again.
We can say:
There are the children enjoying swimming.
(That is they are enjoying it right now. Whether or not they will enjoy it if they go swimming tomorrow is not decided in this sentence.)
And we can say:
There are the children swimming.
And we say:
"There are men running on the track today."
"There is the lady reading the book."
"There is my mom shopping again."
We can also say:
"There is the boy being good finally." ("being good" consists of a linking verb participle plus an adjectival subject complement")
All of the above sentences suggest that something is going on that is best expressed in the progressive tense--that is, something is going on right now; and not all the time, not always.
However, when we talk about, "the children who like swimming," we are talking about children who like swimming all of the time. We are talking about a fact that is true all the time.
We use the simple present and not the present progressive to talk about facts that are true all the time, or actions that are habitual (for example, if the children swam daily, we would say, "[t]here are the children who swim daily;" thus we would use the simple present again).
Usually, if someone likes something, he/she likes it all the time; so you can't use the present progressive tense to say that that someone likes swimming, and thus you can't use a participle ending in -ing to say that the children like swimming. You have to use a verb in the simple present.
"The children are liking swimming better this year,"
is an exception. The children did not like swimming so much last year. This year, something different is going on; that is, right now, the children's opinion of swimming is changing!
Yes, that's fine, if you are talking about this year. And it's important to specify "this year," or "today," or the time period that the continuous (or "progressive," if you prefer to call it that) tense applies to.
But I think of "like" as a verb that is normally used in the simple present, because if you like something, you like it all the time.
If I like milk, I like it today, tomorrow, next week, generally, until I finally get sick of milk (if I do ever get sick of it).