OP, I think you may be missing the main lesson of this incident.
There are a million and one potential reasons why the 3½ year old was in the high chair, and then why her Mum didn't offer the high chair to you. Those possible reasons range from rudeness and poor parenting, through mechanical/logistical issues of adjusting the chair, to some special need (balance, phobia, whatever) that you know nothing about and your friend doesn't want to discuss.
But it really, really doesn't matter at all whether the reasons why your DD didn't get to use the high chair are "good" or "bad". You had an uncomfortable time because you didn't check, when you could have done in a few seconds. If you had done so, you would have had a lovely time with your friend.
Even if you were in the right here, there is no point in trying to prove that, whether you choose to do it in an internal discussion with yourself, or by talking to your partner, or by presenting a case here and hoping that MNers will agree with you (which, inevitably, some won't).
There is an opportunity here for you to choose to think in a different way about what happened, and to realise that you can handle (and often prevent!) these situations differently in future. By asking in advance, you would have saved yourself the hassle of feeding your DD in awkward circumstances, and also avoided getting into a conflict — even if it was unspoken — with your friend, again whether she is actually rude and a bad parent, or dealing with some kind of problem with her DD.
Situations like this will come up hundreds of times in your future life, both with and without your DD (although of course a child always introduces extra randomness). Realising that you can prevent many of them from happening in the first place with just that one extra check or call or question will make your life so much calmer and happier. 🙏