Are you ok, OP? You have received almost 💯% Mumsnet agreement on your question, which must be hard.
But please think of your daughter and your own futures.
“DP went behind my back and bought 2 spiders to keep as pets and the problem is myself and my 16 year old DD are terrified of spiders.”
Tell yourself - this man has deliberately done the one thing that he knows most terrifies both the woman he supposedly loves, AND my child. This is a controller.
“he would sell his property and move into mine”
Tell yourself - we are about to make a drastic move that will be very difficult to reverse when he is living in our home.
“He promised me he wouldn’t and even told me he phoned up and cancelled the order when in-fact he hadn't.”
Tell yourself - he has lied to me twice already over this, and broken a promise, too. He did the thing he promised he wouldn't, and he did not do the thing he claimed he had. This is a manipulative liar at work.
“He said he would get rid of them … he thinks I am being unreasonable asking him to get rid of them and says he will keep them in a garden shed.”
Tell yourself - and the pattern repeats. Said he would do something, did not do it, now he's making me out to be the unreasonable one. This is called gaslighting. And DARVO - Deny, Accuse, Reversing Victim and Offender. Both well known controller tactics.
Lies, broken promises, frightening you and your daughter, gaslighting, controlling and DARVO.
This is a forecast of how shit your life together is going to be. This is his true character and pattern of behaviour.