Chihuahuas are renowned for being one of the worse to toilet train - but, I do wonder how much is due to them being teeny and so being allowed to get away with it. Generally that is a common theme with small dogs, behaviour that would not be allowed in a big dog gets overlooked.
I'm not saying this about you OP, just generally and to point out that Chis maybe unfairly portrayed.
We used to have one, she was brilliant, we always treated her the same as the other dogs and she acted the same - because she was a dog. But the number of people that commented as though that was a strange thing, like Chis were different to every other breed 🙄
You get breed traits, definitely but they are still a dog.
Back to OP, as previously said this is the most trying stage. Besides the energy of youth they go through another socialisation period at this age so it's really important to have positive experiences.
I would recommend 1to1 training with a good positive reinforcement trainer - no negative things like shaking bottles etc. Reward the good, ignore/distract from the bad is always a good rule of thumb.
Only gets attention when all four paws are on the floor, turn away if he jumps up and walk off if keeps going. Don't say anything, they want attention so even negative attention will work. Everyone must do this including visitors, no exceptions. If visitor can't get it (eg too young or just not listening!), put the dog away.
Toilet training - have you tried a house line? A lead that is attached to you so you can be super aware of what he does and can catch him when he's starting to sniff or circle or whatever his cue is. Then straight out and huge praise.
You don't normally have to do it for long, I've never had to use it myself but people I've recommended to have seen results in just a couple of days. Don't forget to keep it up though until the behaviour is ingrained. As Pp said, if he doesn't know that outside is for toileting (and he clearly doesn't) then having the door open won't make any difference.
Also, what are you using to clean up? You need to ensure it's completely broken down as he will still be able to smell it even when you can't - don't use any ammonia based cleaners like bleach for example. You can specially made ones like Urine Off or you can make your own but as he's such a small dog it's probably worth spending the cash on the posh stuff.
You need to check over the houseand try to make sure you get everything you can - if you know anyone with a black light that's the best way although you might be horrified! You may have to do it a few times but if really really persistent and using the house line, you can nail this in a week.
Re DH - he needs to help with the training, best way to bond. Clicker training is great for any dog and Chis are super smart.
And self control exercises will help him, and you. Just Google, there are loads. They will help him make the right decisions as he grows older and learn how to settle himself.
I love seeing a well trained dog and even more so when it's not a breed people expect. Chihuahuas get a bad press as seen as handbag dogs but I know people who do top level obedience, agility, dog dancing and more with theirs. Seeing a little dot charging around the agility ring is hilarious and so much fun (almost as much as watching the sheer joy of a staffie do agility ).
These are little big dogs, they have a heart way bigger than their body and are very capable. Ours was also amazing with children and such a huge character.
One final thing, which is the same for everyone no matter the breed - you will have good days and bad days, even when seems like you're doing everything you should. Don't let the bad days get you down, brush off and keep going but maybe change a gear, do something different, do something fun (scent work, hide and seek, go for a lovely walk, anything). Training sessions should only be 5 minutes or so then take a break.
Ooooo I could go on but will shut up now. In short, it is possible if you want to do this and will only be a bit of work.
Equally, if you have too many other things on your plate don't be embarrassed to say actually this isn't the right thing for us. Have a full and Frank discussion with DH, he has to be on board. Ask why he thinks he isn't bonding?
There are sadly too many dogs in rescue where people have changed their minds and many is because there wasn't the thought there in the first place - but sometimes it just isn't the right thing and it's better to do it now whilst he's at a really rehomable age.