Hi OP, that sounds really difficult. You have two very different DDs and they will each need a slightly different type of parenting. Loving and positive and picking up on their good points for both, but they may need some different "management"; and some of the activities that you can do with DD1 may not be easy or realistic with DD2, or at least not til later.
As well as Explosive Child. you might find a rather old parenting book called "The Parent-Child Game" helpful - it talks about parenting chidren who are "easy", "slow to warm up" and "difficult". It's an oldie but goodie!
I second the advice other people have given you about different activities and play - more physical (large muscle rather than fine muscle), more co-operative games rather than win-lose.
And also, when you tell her to do something, here are some things to try that may work: "when / then" ; "repeat and simplify" ; "threee more and stop" ; "choice of two"; "count to three and consequence".
Repeat and simplify: "DDName, put your coat on. We are going to the park". Count to 10 in your head. Then "DDName, coat".
When /then: "When you have your coat on, then we can go to the park" And repeat, calmly, possibly forever. 
Choice of two: "do you want to wear the red coat or the blue?" Two choices, both acceptable to you.
Three more and stop: "It's time to stop stomping in puddles. Three more and then let's walk on and stay dry - three - two - one - and well done". You can try this for anything that isn't outright dangerous / damaging / harmful to someone else; if it is dangerous etc. then you may just have to intervene physically.
Count to three and consequence - plan out a few little, easy, possible consequences, like losing a few minutes of game time or losing a fave toy for an hour or so, or something equally trivial; then say exactly what you want her to do and exactly what the consequence will be if she doesn't do it by the time you get to three; then count to three slow and steady (one-banana-two-banana-three). If she does it when you say "three", all good. But if she doesn't, you do the consequence. Imprtant things are: do not slow down the count and do not go to two and half, not ever. If you think something will take longer than 3, then say you will count to 5 or 10 instead. You can do it with bribes too - "If you do it by the time I say "three" we'll go for sweeties"
Another one is the "running commentary" - it feels a bit insane but it can work really well. Positive, enthusiastic, warm, reporting on what you're child's doing (well not when they are misbehaving or angry/upset, but just when they're doing something) not praising or judging, just "now you're looking for the shoes, will you find them, you're looking under the stairs, you're thinking, where else to try.... hey you found them!"
To me "never does as she's told", smacking you, and running round shops do say possible neurodiversity, along with your other list of things. But potential rather than definite. So yes, good idea to find out how she is in school. And no harm talking to the doctor, maybe try a parenting group for a range of different ideas and experiences. 