I don't have all the answers as we've got the same here

but I do have various tips to follow if you're not doing them already that is!!
Remember she's only three
Pick your battles and let her see that you do sometimes change her mind over the unimportant things like one more chocolate button when I said only two
Give her simple choices
Does letting her choose her own clothes for the day help at all?
If she's shouting at you don't rise to it (easier said than done especially if the baby is crying at the same time!!) just ignore the shouting...
PRAISE the good behaviour! I forget to do this as often as I should and end up only yelling at her for the bad stuff
Don't sweat the small stuff!
I have to say recently I've just been helping to get her dressed because it's quicker and less traumatic but at the weekend or if I'm busy with Grace I do try and get her to get dressed herself... There are some things that she finds difficult and especially when she's just woken up and not quite with it yet (or had breakfast!!) it's more challenging for her and so she won't even try in the morning...
How about dressinggowns and breakfast first and then get dressed after when she's got some food inside her? Isabelle is a cranky madam extrordinaire when she's hungry!
Try not to do things in a hurry and leave more time for things if you can...
Does it really matter if she doesn't get dressed in the morning? If you need to go out somewhere let her stay in her PJs and there are a few ways it could go - but she will probably enjoy the novelty of it if she doesn't decide to get dressed before you go out for a bit but then realise a)it's cold and b) if it's a playgroup/nursery all her friends managed to get dressed... Certainly the embarrasment factor for my friend of being taken to nursery in his PJs worked a treat but I'm not so sure it would work for Isabelle
Give her responsibilities like putting Kieran's nappy in the nappy bucket that kinda thing - helps Isabelle for sure!
How do you greet her in the morning? If I start with GOOD MORNING Isabelle (in a jolly happy way) fling open her curtains etc then she's usually happier than if she comes to find me and I grump at her and don't want to get out of bed

I think also for Isabelle she's better behaved if I can give her some direct attention while getting dressed and don't just tell her to do it herself because I'm busy - make her getting dressed herself a positive thing instead if that makes sense - so I get Grace dressed first (sometimes get Isabelle to help choose what she wears and occasionally help put it on her too!) and then I can put Grace somewhere safe e.g. the cot or Isabelle's floor with toys and then I can give Isabelle direct attention...
I'm also trying to remember to make time to be fun with Isabelle that's not doing something where she has to concentrate as otherwise I just tend to want her to play by herself and don't play with her focussing on her if that makes sense... Getting her to help (even if it's not convenient to) is a big plus...
I think I've rambled on and certainly haven't remembered all I meant to say but I hope some of that helps as I too am FEDUP of the shouting and grumps and battles!
Oh and getting out of the house early to do something fun REALLY helps as she gets SO bored at home as it's always the same whereas when we've been out and about she's more inclined to play with her toys if that makes sense
Actually one HUGE thing for me is making sure I'VE had enough sleep as I'm SO SO SO much more patient when I have...
I've also been taking the equazen IQ supplements and I think they're helping too! (Isabelle's been taking them too) so helping both of us

Isabelle is such a grump when she's tired and hungry but then again so am I!! Fix both of those for both of us and we get on a LOT better!

I'd better stop now

Oh and have some of these