Or is my husband - doesn't want sex unless stop cosleeping with DC

I agree. The biggest mistake I ever made was co sleeping. Sure the little face and cuddles are sweet. But then you get a child who doesn't want to sleep alone, you feel touched out, and you don't sleep well. I'm sure some people don't have these issues but I did. At 14 my dd still shows up in my room from time to time. I hate it.

Why hasn't the 'spare' room been turned into the child's room?

Then they may want to sleep in it

OP said that DH can't settle his child, not that he won't. I suppose it depends on how that goes. Does he make a half hearted attempt before leaving it all to OP or does OP jump in and take over before DH is given a chance to settle him? It's impossible to say unless OP comes back.

It sounds like he's never approved of co-sleeping so may be annoyed because of that too.

It is not the norm here in the western world where the op is.

I don’t support OP, I think everyone should be back in their own beds. As I mention earlier, we’re currently trying to stop co-sleeping, and it’s horrendous. I completely understand why her DH would like his bed back, I’d like my partner to be able to stay in ours.

It is teamwork, but for me step one of that teamwork involves a transition out of cosleeping.

Of course it's his bed. But it's also his child and he is currently taking no responsibility for the sleep training and withholding sex until his wife figures it all out on her own.

Is everyone forgetting that the child is his too. It's like the 1950s in here.

And you wonder why he is fed up? Most men would be thoroughly pissed off to be kicked out of their bed and sex on hold because you refuse to train your child to sleep in his own bed and put your excessive attachment to your child above your marriage.
Sex is a normal and healthy part of a marriage.

No, we just don't have sex

Because it's his bed too. Kicking him out of it shouldn't be an option and certainly isn't teamwork either.

Part of the agreement could be DH agreeing to work together to sleep train or at least start 3yo out in his own bed so they can have a few hours alone in bed together.

Some marriage!

YABU.

What about other people's wants? Why is this particular issue one where his wants trump everyone else's?

For ops dh there's no solution where he has to do anything, which is convenient. She has to meet the child's needs differently and deal with the fallout on her own, so that she can then meet his needs. That's not intimacy, or closeness, or teamwork.

You can literally just keep flipping your argument to support OP.

It's about teamwork. If DH suggests that OP can have a lie in, nap or early night because of the night waking then that's team work. If he purely just wants the bed and doesn't want to help with night waking then it isn't.

No, we just don't have sex

DC is just under 3. Cosleeps with us for about half a year now.
I love the cosleeping - it leads to more sleep for me and in all honesty I love waking up to the tiny sleepy face or the little hugs I get in the middle of the night, DH not so much - he occasionally gets woken up by DC turning over in the night and DH believes a bed should just be for parents.
We have a large and comfortable sofa (for sex or to sleep in) and a spare bedroom (which, in fairness is full of clutter and used as a storage room but has a bed).
DH has declared that he is uncomfortable having sex when a toddler is in our bed. Understandable. To my suggestion that there are other places to have sex he's said he just likes it in a bed, after a cuddle rather than a scheduled walk to the second bedroom or on the sofa.
DC sleeps through the night when we cosleep but wakes up every couple of hours if we sleep apart. Inevitably I'm the one that has to resettle DC if they wake up because DH absolutely can't (DC will not go back to sleep, just gets more agitated). If we were to end cosleeping I'd just end up marching back and forth between our room and DC's all night, or camping in DC's room.
So... who is being unreasonable? Him for wanting DC out of our bed and threatening no sex until I do or me for not wanting to kick DC out? What solutions do I have? I do want sex, in theory could easily live without it but it's not great for a marriage to be sexless.

Why is this particular issue one where his wants trump everyone else's?

Because he’s the other half of the marriage and he gets an equal say. The toddler doesn’t get a say.

So should he be evicted from the bedroom so it can continue?

That’s a super quick way to disregard someone, and could lead to some real relationship problems.

No, we just don't have sex

She wants to sleep with her toddler.
She wants to be able to get rest at night and not have to be woken from a toddler.
She wants to have sex in the spare room or on the sofa instead of in the bedroom.

All valid reasons. Reasons why plenty of people co-sleep.

Maybe we should get the toddlers opinions added too.