I know where you're coming from. My DH has a job that means he travels a similar amount to yours, and often the trips are at short notice which means cancelled plans etc. Mine had to spend 3 weeks on Australia when I was nearly eight months pregnant, I still remember the very minute he told me about that trip! I know also that long haul is more disruptive. You count on there being two of you the day he's back but actually he's struggling with jet lag so it takes out more days than you'd bargained for. Personally I find those days are harder, when he's not there I don't expect him to help, but when he is, I do, even if he's tired. I couldn't comment, obviously, on the rest of your relationship and what else might be at play here, and obviously my husband isn't yours but for what it's worth (because believe me, I have deeply resented his job, but I have made a kind of peace with it):
it does get easier when the kids are bigger, really, truly it does. The stage you're at is the worst but you will get your own routine with the DC, they will get used to having DH away and they will be just a little bit more independent (my DC are bigger then yours but not really big and we have a completely different but completely normal routine when DH is away and have done for some time)
what are the chances of a new job also requiring travel? Some careers do, it's the whole line of work not just the company, so even if he moved, would it actually give you what you'd like? Again, my DH isn't yours, but I have to accept that a new job for him is just different travel, it'll never be no travel. We're on job 3 of our marriage, all with travel, his, not mine.
If this is really the only thing as your original post suggests, can you (both - and the both bit is really important) put your energies into how that time he has to spend away can be easier for you so, can his family help out as well as yours? Do you have a babysitter - or can you find one - so that you can have something you do regularly that can carry on regardless when he's away? What do you need from him when he's back? Do you need some time (evenings, weekends, etc) away so you can have a break?
Are there some dates/ times that you really need him home that he can stick to - and yes that might be a difficult conversation for him at work from time to time,( but in my world it's nothing more than I do when I have to do all the sick child cover when he's away because there's no-one I can share it with)
Can you still speak to him properly when he's away? Time zones can be a challenge and to be honest after a full on day there are times I'd rather have a nice quiet evening by myself rather than a call. But it is important to know that if something comes up that you need to talk through with him, that there'll be a way to do that.
I wouldn't necessarily recommend moving closer to his work, unless that works for you all for other reasons, the issue is the travel but not the commute, right? So moving closer won't change that and you'll lose your support network. Sure you'll get another one but the effort is maybe not what you need right now.
A big thing is how much he likes his job, sounds like he's doing really well and he's obviously well regarded (why does it matter how it got it? Seems irrelevant?). He doesn't sound like he really wants to change - and to be honest, if he loves it as you say and he's getting on well I'm not surprised he doesn't - so you probably need to both focus on how to make it work for you. It's hard because actually the travel is probably quite gruelling for him too, so he may well not get how hard it is to be left at home - I know this has been a recurring theme for me, but don't feel guilty, you're doing a full time job at home, you need a break as much as he does.
Your comment about "lack of control" struck a chord with me. You can't take control by insisting he leave a job you say he loves. But there are lots of other ways you can get some control back. Best of luck, and remember you are definitely not the only one with a travelling husband, not matter what your current circle of friends makes you feel.