I'd make sure you contacted the management telling them you were going somewhere else and suggest they train their staff accordingly.
What have the staff done wrong ?
. They were asked by two other swimmers to have a word with someone who had pushed between them. Very rude and potentially intimidating.
If it isn't a pool party or a waterpark, then they don't have the right of hogging a public pool to have a chat.
Of course they do.
Not that they were 'hogging' - they were swimming, just not up at the speed the OP would have liked. Are you seriously suggesting you have to pass a swim speed test before being allowed to use a public pool ? 
The clue is in the name: they're called 'swimming pools' for a reason.
Well, round here, people talk about going to "the baths" not "the swimming pool", which rather rules out that argument.
If she was 'rude' for swimming between them - and I can't see why this should be the case
Are you for real? If you are walking down a pavement between 2 people walking more slowly than you, do you go round them or barge through them ? If you seriously think it is okay to barge between two people having a conversation, you need to do some work on your social skills.
In response to some other quite strange posts here in relation to the 'right' to socialize, float about on lilos etc, I disagree that this is what pools are for (training/baby pools excepted). The general situation in any standard 25m pool is that people will use it to swim up and down its length. Go to any of them and watch what people do
Not in any of the pools I've ever been in, except during the lane swimming session. Yes, some people swim lengths, but pools are used for kids to play in, people to practice their widths, people to practice jumping in, people to spend time moving limbs with the pressure of water, people to practice picking things up off the bottom of the pool, or fun stuff like swimming under peoples arms and legs, people just having a rest inbetween lengths, parents who have to accompany U8s, but who really don't want to swim, pootling around waiting, etc, etc.
And faffing around, swimming and chatting, congregating around one end and generally causing an obstruction and annoyance for other pool users -
You mean, 'relaxing and enjoying themselves ?