Hello and welcome! I think the answer does depend on how likely you think the relationship will work out. Evidently your girlfriend is wondering about that, too. Yes, you are right that it's not a good idea to introduce kids to a new date one after another.

It's been a year. I would think you would have a good idea by now about whether she is "the one." Are you hesistant to ask her about the "marriage" word?

Would she accept the idea that you are introducing your kids to a "girlfriend who MIGHT one day be their step-mother, but you are and she are giving it some time to see how things go"? Or more that she is a "girl" and a "friend"?