D..
Well, I've been waiting for someone else to write in, but no one has. I've been thinking about this question for about an hour now...
I would try swim lessons next summer, but not ones where the parents are part of the group. You should not be there so that other adults can work with her. Part of her behavior is because you are there.
Is your daughter in preschool? If she isn't, she should be in a half-day program. You need to send her well before going to kindergarten so that she can learn to get along with other kids. AND, she needs to learn to follow the rules with other authority figures, without you being there. She will need to learn to be with other kids so that she can get through kindergarten. Getting her school-ready will be very important. You can try programs with small groups of kids to start... If she cries about going, just drop her off and leave. No trying to calm her down. Let the preschool do that. They are used to this with kids. And kids do eventually learn to do this.
I would talk to the preschool director and tell them everything you have said here. And if I were you, I would no longer respond to her pointing, grunting and crying. She is old enough and smart enough to communicate in a different way. What she seems to be doing is trying to get more attention out of you, make you "jump through hoops" to get her to work with you. And it's time for you to stop allowing it.
It's like when a child has a tantrum. You take yourself out of the equation so that he or she has no more audience. You put the child in a room and leave them, without talking, until they are done. It might take a good while for them to finally realize that they won't get anywhere acting like this, but keep being 100% consistent. Don't give in. It's really important that you don't. And if she does this while you are out somewhere, take her to the car, strap her in her seat and stand outside of the car "reading" while you ignore her. (Not if it's too hot outside, of course.)
The thing is, all this attention you are giving her, trying to get her to communicate with you for 20 minutes, is just egging this behavior on. Instead, tell her "I can't understand you when you point...grunt...cry" and walk away. If she escalates to a tantrum, then put her in her room and don't allow her to come out until she is done with the tantrum.
The ball is in your court and you have to help her grow out of this by not allowing it anymore.
If you continue to have trouble with her after several months of consistent parenting, then I would take her to a child psychologist.