We have been looking for a bigger place to rent because the house I own now...
She is forcing you to get a bigger place maybe with her name on it. Give her a time line, and plan for that to happen, or put her name on the deed after you marry. If she doesn't go for logical solutions, then its you who should have cold feet. I think she is trying to hedge her bets here guy, JUST IN CASE, it doesn't work, she doesn't have to move her kids out of a house YOU own.
Don't get married until a solution is reached. A woman with 3 kids is not about to put their security in jeopardy, and don't expect her too.