My marriage is in trouble

My husband and I have been married 8 years. We have a 5 and 2 year old and a baby on the way. In the past my husband has cheated. I think he should let me have passwords to email, social media, etc. I also think he is distant and moody. He lies to me frequently. I don't want a divorce but I feel powerless to change anything. He lies and I get upset and cry or yell. He doesn't seem to r remorseful. I need advice

Yes, he should. And no, he shouldn't be. And no, he shouldn't be. And no, he shouldn't. And yes, he should. And yes, evidently you do. If you don't (yet) want a divorce then insist on a 6 month separation in which time he must make the firm and committed decision to act like a HUSBAND who has nothing to hide and doesn't wish to keep his own supposed soulmate out of a significant portion of his inner life, as well as one that gives a damn when his suspicious behaviour constitutes twisting the same knife with which he originally stabbed her. ...but I don't fancy yours much, I have to say. So I advise you to have a free consultation with a family law solicitor anyway, just in case, just so you know exactly where you'll stand if it comes to it. The surge in your confidence might well make ALL the difference to whether he cleans up his act while he still can.