Some Christian groups hold something like a "seder" on or near Passover. A Christian asked on Mi Yodeya whether this is offensive to Jews and, more generally, how such groups could celebrate a Christian seder that would be acceptable.
An ex-Christian once described to me the seder that her church did when she was growing up. It was adapted from the haggadah, the text that we Jews use, but it had some Christian overlays. I don't know if all Christian seders do this; from the description in the question it sounds like this is not uncommon.
Adding Christian symbolism or theological claims to a Jewish practice feels to many Jews like misappropriation. You see this in the deep, visceral reaction that many Jews have to "Jews for Jesus". It's not just that they're luring Jews into Christian worship but that they use the symbols of Judaism to give the impression that what they're doing is compatible with Judaism. (Many of us consider what they do to be fraud.) In a similar way, a Christian "Pesach seder" that likens the three matzot to the trinity or to the eucharist, the pesach lamb to Jesus, or anything messianic that is not entirely in the future, is problematic. In my experience, most Jews who are aware of these alterations would be somewhere between extremely uncomfortable and offended.
You, as a Christian, want to celebrate the history that our religions share. Further, Christianity holds that a key event in your religion happened on Pesach, so naturally you want to celebrate that. I get that. I have a suggestion for you to consider: study or re-enact your traditions for that night -- a re-enactment of the "last supper" rather than a Pesach seder, in other words. After all, you're celebrating Easter, not Pesach. Even if you hold that that meal occurred on Pesach (which doesn't work from the perspective of Judaism, but Christians might not be concerned about that), the Pesach seder of 2000 years ago was not the same as the seder we know today.
If that suggestion doesn't appeal because you want to hold something like a Pesach seder because of your historical connection to Judaism, then consider studying the Pesach seder in an interactive fashion. You could actually do many of the things that are most engaging (especially for children) -- songs like "Dayeinu" (it would have been enough) and the four questions, the recitation and possible re-enactment of the plagues, and learning about and eating the symbolic foods. To this you could add a reading of the text from Exodus. Further, there are parts of the traditional Pesach seder that would probably make your eyes glaze over because they're steeped in traditions of Jewish study that will probably be unfamiliar to you -- so go ahead and skip those. Don't think of it (or bill it) as "having a seder" but instead "studying the seder, with selected parts". (One detail: it would be best if you did not say any of the blessings that contain the phrase "Who has commanded us", since (a) you're not actually holding a Pesach seder and (b) you weren't actually commanded.)
A Christian seder that looks sort of like a Pesach seder but is actually Christian in nature is very likely to bother Jews who know about it. But this doesn't mean you can't teach your community about Pesach if you want; I presume that you teach other parts of the Tanakh (what you call the "old testament") too. The key is truth in advertising; a Pesach seder is a Jewish, not Christian, observance.