Should I take this lie detector test?

Anonymous
I have been in a relationship on and off for 4 years. He is the father to my children and I do care for him but I think he is going quite far asking me to take a lie detector test over a guy I talked to a long time ago who I was only friends with. He claims he is not a jealous man but if he sees me talking to a guy he acts up. I have tried making gay guy friends but it is a little difficult so if my guy friends are straight it should not be an issue if no sexual interactions is involved.
I think the part that upsets me the most is that he was caught in multiple infidelities in our relationship including sites like tinder and sexting other women behind my back.
When I try to bring it up, he gets defensive and wants to avoid the subject by giving half responses but when it comes to me on anything he wants full explanations which has led to this polygraph test.
And of course I will note I have let him go through my phone before to prove my innocence and let him read it in front of me but still to no avail.
I also recall an instance where I wanted him to be honest and show me a message where he texted a woman on tinder and I wanted to see them. When he came back, he told me it was deleted and I was super furious.
What would you do in my situation?
Should I take this lie detector test?
2 Opinion