The mind of Howard and Spoilers of Course

Theres many unanswered questions of the movie, and some interesting decisions made by Howard. When I first watched the film, I considered that Emmett and Howard were working together to trick Michelle and maybe the ultimate scheme was Howard would be the father figure/god and Emmet and Michelle were going to be his "Adam and Eve" but as the film progressed we see and understand that Howard built the bunker with two intentions
1) To kidnap and hold girls hostage to replace his estranged daughter
2) For actual doomsday prepping based on his conspiracy theories and secret projects in the military.
And Im going to expand on both.
I will refer to the timeline that can be seen in the special features of the film.

Howard kidnapped and held the girl Brittany that he calls "Megan Prime" since 2012, and the events in the movie take place in 2016. So that is four years time he could have held Brittany. Emmet said he helped him build his bunker but didnt give the amount of time he helped or what year. So By looking at the actors age he wouldve been 32 in 2016, so if we compare his age to the bunker timeline we can speculate what years he could have helped. Emmett would have been 18 in 2002 and thats also when he said he purposefully missed going to college and stayed within the 40 mile radius of his home. This means Emmett could have helped Howard on and off from 2002 to 2008, as the timeline states that by 2008 the bunker is basically finished as it lists the last rooms built. Emmett gives Michelle important info when he immediately recognizes that girl in the photo as the missing girl Brittany who "went to school with my sister". Now if Emmett was helping Howard for several years then its quite possible that Howard saw the girl Brittany through acquaintance with Emmetts family. AND this timeline along with Emmetts quick recognition poses an interesting question!

When did Howard Kill Brittany (Megan Prime) and also why?

Michelle finds the word HELP carved using earrings on that small outer dome near the backup escape hatch. People pointed out Howards stupidity of not seeing that carved there when it was ground level, but what if there was no time to see it? What if Brittany carved that there in 2016 just a day or two before the Apocalypse and Emmett's and Michelles arrival? What if Brittany climbed the air ducts and wrote the message, but out of desperation for food and water she reluctantly climbed back down to face Howard, only for Howard to lock her up somewhere. This also explains why the main hatch to the HVAC was blocked as Brittany would have blocked it to keep Howard from coming up to get her while she carved the message for help. And notice Michelle never unblocks it as she discovered the HELP message and realized Howard is truly a nutjob. Michelle could have told Howard "oh the hatch is broken" but we never see that conversation on screen. After Brittanys escape attempt, and recapture, the apocalypse happens and Howard kidnaps Michelle as a means to placate Brittany and give her some female company so she wont try to escape? Or worse case scenario Howard kindaps Michelle because he wants a "Backup Megan" since "Megan Prime" (Brittany) is not working out? It fits into Howards psychology of having backup plans and preparing for all scenarios. BUT here is where Howards plans lose options.

Emmett shows up and fights his way in! Now why wouldnt Howard just kill Emmett right then and there?

It could be that Howard grew to know Emmett those six years he helped him build his bunker and realized that Emmett could prove useful in the future for his construction know how. Also he could have realized that Emmett knew this bunker better than anyone else besides Howard himself, so if he didnt let Emmett inside, then Emmett could compromise the entire safety of the bunker by breaking inside another way. AND Howard could have quickly made a decision that works in his favor...He was kidnapping Michelle as a "friend" for Brittany to placate her, but now he has Emmett. So he decides
"Emmett can be useful, he is more dangerous to be left outside as he can break in another way, and he can be a "friend" for Michelle to placate her so he doesnt end up with another girl trying to break free like Brittany did".
But what does this mean for Brittany who is locked up tight? Howard cannot let her live anymore as he knows Emmett will recognize her immediately and she'll turn Michelle against him as well.

This could explain why he let Emmett live at all, as we can see in the film he finds Emmett irritating.

But maybe Im over-analyzing all this? Maybe Howard killed Brittany just a day or two before the apocalypse and he grabbed Michelle as a quick unplanned effort seeing how he wanted a "daughter" with him in his bunker and he is out of time to search again? It still fits with keeping Emmett alive for the time since he can prove useful later with his construction skills.