We told family (our parents and DH's siblings) and our line managers at work due to the practical requirement for time off to attend appointments. Nobody else. Our line managers were great but obviously just on an arm's length professional level, which was all we wanted from them. Our parents were supportive, but there was a barrier because they were so very worried about us, and we wanted to protect them a bit from being worried. (I wonder if being worried about you, or not wanting to show their own feelings and burden you with them, is part of the reason for your parents' apparent distance - are they the stiff upper lip generation?)
I needed to talk, but chose to have a lot of counselling appointments at the IVF clinic instead!
However...We had one failed fresh cycle (chemical pregnancy) and one successful FET. I had bleeding through the first and into the second trimester and told selected colleagues/friends on a "need to know" basis, as for me that felt easier than the pressure of concealing what was going on. And I was lucky to find some wonderful friends and colleagues who knew the right things to do and say. The support was so lovely that I sometimes wondered if I should have been open during treatment. But on balance, it was right for me not to be. It's always risky telling people about infertility, IVF, pregnancy issues, or losses. You have to be prepared that some people you trust with the information, just won't know what to say, or will say some very crass things, or simply won't be there for you. (My BIL and SIL weren't, and that sort of thing festers for a long time.) You also have to be prepared to share bad news in "real time", as well as good news, and for their reaction to the bad news to be unhelpful.
When I told the world at 20 weeks that I was pregnant, I was matter of fact about it being an IVF pregnancy, and I continued to be open with people after DS was born. Not least, to show what solidarity I could (from the pregnant side of the fence) with people who might, unknown to me, be going through their own infertility struggles. And so many people I thought I knew well have said said "oh yes, me too" - either currently ttc and having problems, or that they'd had a child following infertility, or had experienced secondary infertility. I have never regretted starting those conversations. Infertility affects so many people but there is such silence around it.
However, when you're in the midst of treatment, your focus needs to be hanging in there from day to day. Awkward or crass responses from people you trust, are just too much to cope with. So I'd share the information very cautiously. Having a few people who know, who you can lean on, is good. I hope you find them And good luck for the cycle.