You're in a very difficult period of your relationship. Many/most of us go through this time. It sucks. But the good news is, it's not permanent.
Most of our marriage, my wife and I worked opposing schedules (made it easier than using daycare), and we raised 3 kids. So yeah, sometimes it felt like we had no time to connect. Sometimes, one or both of us felt neglected in the bedroom, or just intimacy wise in general. The important thing you both (more your husband right now from what you say) need to keep in mind is this is not personal! It's just a challenging time.
Yes. It can be frustrating. And it's very easy to begin feeling like you're being neglected intentionally and maybe start feeling resent if you don't keep perspective. You're used to how it was in the beginning, and seemingly overnight, it slows drastically. But that's only due to your life situation. You and your husband should make time to touch base with each other. Check in on how the other is doing. Reaffirm your love for each other. And equally mourn your lack of "quality time" together. But keep in your minds that this isn't forever. When the child(ren) get older, and more self-sufficient, some of the current obstacles will go away. In the meantime, it doesn't hurt to try to set aside a night where the 2 of you can have some quiet time together - whether sex happens or not. Just some alone time goes a long way.
Time to have a heart to heart with your husband. And you can tell him from an old(er) man who once was where he is: he needs to understand that life will often get in the way of having the frequency or even quality of sex life he wants right now. It doesn't mean you love him less or don't care. It sucks, but he's going to have to "take matters into his own hands" more often than not if you know what I mean. And I know a lot of men bristle at this next bit, but the sooner he accepts it, the better it'll be: he needs to go the extra mile and take stress and responsibilities off your plate. Even if he thinks he already helps out enough, doing more allows you to get in that headspace. It's not a "do these chores and you'll get sex" thing. It's making sure you're not overtaxed and stressed. Even under the best of circumstances, he's not going to get what he wants as often as it was in the beginning. But he may get it more often than he currently is. And you need that connection too. He's not the only one feeling that way. Tell him from me that he needs to be more affectionate WITHOUT expecting it to immediately turn into sex. The more he presses for sex, the more he's going to drive you away. By relaxing and letting it happen naturally, he may not get it often, but it'll be much better when it does. And by being more affectionate, it may not lead to sex that day, but it can make you feel loved and build some desire over time. (And let's be honest. Men need affection too)
On your end, don't have sex just because you're expected to. Ever. If it's not good for both of you, it's not good for either of you. That said, try. What I mean by that is engage in some light foreplay (kissing, caressing, etc) and see if you find yourself in the mood. Don't just wait to actually be horny before you even start. You may surprise yourself some days. And if after a few minutes, you're just not feeling it, well, it's not the night.
And your husband could stand to learn how to read the room a bit. Asking for sex when you're in a bad space emotionally is not good. It's putting his wants and needs in front of yours with no consideration for you. I understand the thought process of needing to maximize the opportunities you get, but there are times when that doesn't apply. And when someone is mourning is definitely not the fucking time!
I said above that the good news is it isn't permanent. That's true. But it's only true if he handles this time of your lives well. Get pushy, be resentful, petulant, etc, he's only going to drive a wedge between you. Then, when what can be good times rolls around, it'll be too late. You'll have grown apart. Get it in his head that you're both going through a rough time and be patient and understanding, and your bond will grow. Then, when the good times come around, it's almost like another honeymoon phase.
No. Men don't automatically cheat just because they're not getting as much sex as they want at home. Well, good men don't. He has 2 good hands. He can even buy toys to help take the edge off if release is that important to him.
I don't mean to make it sound like he's the only one that needs to do anything here. You're both going to have to work together to try to keep that flame alive. But it can be done.