First thing, whatever you write don’t lie. It’s one thing to presume something, a different thing to vocally affirm it far beyond the strength of one’s actual belief.
Next, don’t put that person in the awful situation of having to clarify and either expressly tell you aren’t invited or actually invite you in order to avoid the awkwardness of that.
Don’t presume bad intentions — people sometimes omit invite some of their relatives or friends in order to avoid awkward situations with other relatives or friends or for some other similar reasons, or perhaps because of costs or lack of accommodation, or sometimes because they feel like being alone with their immediate families for Christmas. It could be awkward and painful for them to have to state their wishes clearly and hurt both the non-invited relative’s feelings and their own. If they choose to be delicate about it, it’s their preference and it should be respected, or in any case it that merciful shroud of mystery that leaves some things unsaid seems to be what they currently need. Or at least ask for. So even if you don’t think they have a right, you could still be inclined to grant their implicit request.
Easier said then done, I know, but what helps me in those situations is to bring back memories of myself acting that way or in a similar way, or almost, or finding similarities between how they are acting and some things I’ve done.
Re: ‘assume’, unless your relative is a philosophy or science major (and perhaps even then!), the word probably wasn’t used in a strict way and the whole sentence was the product of some thought but no overthinking, so analysing it in such a way as though every nuance were intentional and premeditated it would make little sense.
Finally, like some other posters, I’m not even sure that really was a disinvitation (it looks that way, but I’m not sure). However, I can’t think of any way of asking that wouldn’t lead to a lot of drama.
Merry Christmas to you (we’re already celebrating in my family) and hope it can still be happy indeed.
The world is a small place sometimes.