OP, you've got your DD in nursery 3.5 days and with your partner and dad for another 1.5 days of the 5 days you work. Its a juggling act and well done for doing what you think is best. At the end of the day, all of us as mum's make decisions based on our own circumstances. I'm a SAHM and the decisions we make to be SAHM, work FT or PT are rarely easy. Don't feel bad for those decisions.
Re the behaviour, I do think there needs to be a multi-approach to it. Firstly understand the behaviour, many have pointed out that your DD is probably tired, wanting mummy and also acting out in the knowledge that regardless of what she does mummy always loves her.
I'd also consider if she needs food - my daughter when I collected her after school at 3pm could be a nightmare but after a quick bit of toast or packet of quavers or whatever I had to hand would settle into a more manageable child. The power of food can be amazing. I know the temptation is to say no, its almost dinner time, you won't eat your dinner. But do try it for a few days, see if it makes a difference.
Also, is there a day or days where she is worse than others. If so what happens those days (is it an outdoor day at nursery, is it the day with grandad, or a particular care worker who does specific activities that she does or doesn't like)
Once you understand where the behaviour is coming from you can try to adapt to deal with it (give food, be more prepared on those days, change the time of swimming to earlier/later etc)
Speak to her. Praise her, tell her what a big girl she is getting, all grown up and understands what it is to be good, naughty. Try to get her to explain why she behaves a certain way. There is an episode of Wooly and Tig where Tig is very badly behaved because she is tired. Its a great springboard for the conversation I found.
I definately agree with the others that unstructured time at the weekend is vital. I know some people find a need to be out the whole time, letting kids run around the park and for some kids this is absolutely needed. But it doesn't work for all, it doesn't work for me. We tend to stay in jammies till late, I let the kids build train tracks or duplo villages, paint at the kitchen table, get the playdough out etc. Involve her in the household stuff - let her 'wash' the dishes at the sink (yes you'll have to put them in the dishwasher after anyway!), sort the colours of laundry. It will take you longer but it will help you reconnect with her and get back that feeling of not constantly saying 'no' or yelling at her for doing wrong.
Once you manage to reset then you can get to a point where she knows its not acceptable to act out because she is tired. She will still do it, but she'll start to understand what is happening, why and be able to articulate it with you. My daughter at 6 will now just crumple with me sometimes and say 'I'm grumpy because I'm tired....." to which the response is, that's ok, we can deal with that, lets get jammies and the snuggly blanket and have a mummy snuggle.
Finally someone mentioned about the pebble idea and I do a similar thing, we have a little wall ornament with pegs and the kids little named shaped hang on them - there is superstar, oops and oh dear. They start every day on superstar, for minor issues like not listening, or doing as told, they go to oops. If they are really naughty, like hitting each other, throwing things they go straight to oh dear. At the end of the day if they land on superstar a cotton wool ball goes in their jar, for oops nothing happens, for oh dear they lose a cotton wool. Obviously they can move up the chart as well for good behaviour after a naughty even earlier in the day. When the jar is full they get a treat, it might be a comic or book, a toy car or a specific sweet.
I hope you get it under control. Its not easy and you are right they can be a total PITA when they are like this. But you can get your lovely girl back, I promise xxxx