I think you're really onto something when you point out that these things are genetic and so to us as parents it can be really hard seeing professionals pathologise behaviour or preferences that are just natural to us. I certainly found that and found it very difficult to accept that she was autistic - to me she was just DD - sensitive and lovely and more interested in books than the rough and tumble of other kids.
It can also be very hard to disentangle Autism and ADHD as there are many overlapping sensitivities - both can come with hyperfocus, sensory sensitivities and executive function problems, for example. Many many people have both (see e.g. Purple Ella here - she also has a bunch of other videos you might find useful if you subscribe as she is autistic/ADHD and has autistic kids: ).
Meltdowns and controlling behaviour tell you that your kid is getting overwhelmed, but not why. It's good that she's having a better week and being overwhelmed less, but to my mind it is still definitely working out what is at the root of that so you can avoid it in future. A close friend was just told their daughter likely has ADHD and ASD. The ADHD is fairly apparent (and like you, runs in the family) - the ASD is much less obvious, possibly because it is being somewhat masked by the ADHD. This is a very social and confident child - but the EP sees enough differences in her communication that they think it is worth exploring at least.
And that is all a referral means - that it is worth exploring whether this is an explanation for what your child finds difficult, and how to help them.
I realise there is a certain stigma for ASD diagnosis (more so than for ADHD I feel) but honestly I think things are changing massively for the better on this. Look up young autistic women like Elle McNicoll, Camilla Pang and Abigail Balfe - all now writers but all had successful careers before that in different fields and are clearly very accepting of their brains and both the challenges and gifts that come with that.
In the end we are very glad to have DD's diagnosis (she is now 8). She is doing really well (happy at school and at home, with a few good friends) but some challenges still (mainly around anxiety and overwhelm). Although school should make accommodations with or without a diagnosis I'm sure it's helped us to get more understanding for her and some supports around transitions and planning because we have a clear diagnosis from when she was young (so they don't just blame bad parenting or an over-sensitive or over-indulged child).
Even more importantly, it's given DD a really good understanding of herself. There are some great books for kids now (including by the authors listed above) to help them understand their wiring and why they find certain things hard (e.g. sounds, transitions) or have certain abilities (e.g. hyperfocus, creativity) that come along with their Dx. Understanding that you're just "different" not "wrong" is incredibly powerful and a gift to any child.