Yes, you do sound possessive. What makes you say that this guy Mark is not necessarily respectful of her? Just because they are starting to get to know each other? He must have moved mountains to arrange this trip if he's a single dad, so obviously there is some motivation there. Ya gotta start somewhere.
Let her manage her relationships and you manage yours, including the one you have with yourself. Try to take a look at why you feel superior to and competitive with this guy. What does it bring up for you? Fear of loss? Just a change in your environment and feeling out of control? Dig deep, but don't expect Tara to make you feel better by giving up something she wants - that would only be a Phyrric victory and you'd have "won" but would feel like shit about it. If, after a few dates, she feels like she and Mark have something and they wish to continue seeing each other, I am sure she will want to introduce him to her other partners. But to make it a requirement? Ick. Kinda dictator-ish. You don't want veto power, do you? She should be able to be involved with whomever she feels drawn to without needing your approval of who that is, I think.
The world opens up... when you do.
Oh, oh, can't you see? Love is the drug for me. ~Bryan Ferry
"Love is that condition in which another person's happiness is essential to your own." ~Robert Heinlein