She may just be tired and need a nap.
Children at this age, still benefit from a nap. My girl is 5 going on 6 years old, in the 1st Grade, and still naps after school. She is napping now in fact.
Kids this age are tired after a full day at school... they come home and need to deflate and unwind. For my girl, we come home, I give her a meal or snack (she is famished after school), then I let her choose what she wants to watch or play with and let her have time to unwind. THEN, she takes a nap. She is t-i-r-e-d after school and will even tell me she "needs to nap."
THEN, after she naps, we do homework. At this point, after being rested, she is MUCH more attentive and can focus. Otherwise, she is just too "over-tired." Overtired kids are actually more "hyper" and fussy and grumpy and argumentative....AND distracted.
This routine works for my girl and me. It's much less of a struggle.
I noticed that you said "she" does homework in the kitchen....or "she" tried going in her room to do homework etc. - so it seems like it is a "she" doing homework by herself thing... versus a "we" work on homework kind of thing. THIS MAY be the "problem."
For example:I sit with my girl in her room at her desk, and WE do the homework. At this age they still need us to help them.... and answer any questions. Sure, my girl does her homework by herself... but I am there for support and supervision and clarifying things. I actually sit there with her. This way, she is more inclined to feel actually doing it, and "we" get her homework done quicker that way.
At this age, I still feel a child needs the Parent to sit with them and do it. They are independent but not that much so to where they can regulate themselves.
Perhaps also, she seems to have a lot on her plate as far as scheduling??? I'm not criticizing... but at this age, they can really get ragged. And if she is missing her tv time... then maybe something has to give???? Kids need downtime... and just being. It's important for them to just be, too. Maybe she can take her gymnastics on the weekend instead? ..I imagine that after a long day at school, then having t do homework before gymnastics or the pool... then after that's done, coming home, at night, being tired after all that, THEN having to get ready for bed and that whole routine.... when and how can she just deflate or hang-out and unwind? And by this time, she must really be tired or worn out.
For my girl, she also needs time to chat with me afterschool... that is her way of re-grouping about the day,and it relaxes her. So that's what we do. ALSO, it never works well when I "rush" her to do things or get her things done. Rushing my girl NEVER works and it only makes her more frustrated... hence we can't get focused on her homework. I have learned to "know" her rhythms... and how she responds best in order to perform. Each child is different.
We do the SAME routine everyday... and so I rarely have to force it or pressure my girl to get things done and it works out.
If your girl is taking 2 hours to finish 2 worksheets... SOMETHING has to give. To me. For 1st Grade... homework is not meant to take 2 hours.
I think your girl is just too tired after school to focus. I really feel she "needs" some down-time. And maybe hungry too, maybe she needs more than a snack after school. Remember, in 1st Grade lunch is early (at my girl's school, 1st Grader's have lunch at 11:30, and school ends at 2:15. (and usually kids don't eat much in the cafeteria, sometimes none at all). That is a long time to go without a snack or another "meal" for a child. They are active in school, physically & mentally... and by the time they come home after school, they are hungry and thirsty and tired. That combination of things does not make for a "focused" child.
Good luck and all the best. Just some ideas about what we do, and seems to work with my girl. Sorry for rambling...
Susan