Can't cope with my child, suicide seems the only option

I think you've taken a brave first step to come here and open up about your struggles. 

You're dealing with a lot, so you should definitely seek some further help & support. If you speak to your GP about how you're feeling (including the suicidal ideation) they should refer you for some therapy / counselling. I know it won't make all the practical problems go away, but mental health support is very important to help you deal with all of this.

Also as people have mentioned you should be entitled to seek support / diagnosis for your son without his Mum's approval. You can make an appointment with his GP to talk through all the issues around his behaviour and ask for a CAMHS referral for a diagnosis. 

While you're waiting, I'd suggest it's worth making the assumption he probably is autistic and start to put some strategies in place to help deal with the most challenging issues - there could be 'workarounds' (for example my daughter has a sink wash with a flannel rather than a shower, as showers terrify her) Every little struggle you can find a workaround for will make your daily life a little easier. Also does anyone at the pre-school have knowledge / experience of autism? Maybe they can help? 

1. Your child is not 'bad' he is (probably) autistic. I feel I need to emphasise that.
2. As his father you've every right to talk to his GP and ask for an autism assessment. it would be better if you could do that with your ex wife's blessing but you don't need her permission any more than you'd need her permission to take him into the GP if he had a rash or stomach ache.
3. Again your own mental health seems to be suffering and you might want to talk to your GP about that.
4. Having an autistic child can be stressful but you will make your interaction with your son a lot easier for him and you if you try to understand what drives the 'bad' behaviour of your son in specific terms instead of just trying to classify it as generic naughtiness
   1. for example he misbehaves on outings well what about these outing stresses him out so much. If you put some effort into addressing the stressors and triggers of his anxiety it will be easier to deal with his behaviour.
   2. Autistic people often process sensory issues differently to normal people. So take a bath for instance. What seems pleasantly warm to you might be far to cold or hot to him. The nice lavender smell of bubble bath might be a pungent and unpleasant oder to him. The sting of soap unbearable. Maybe he's just uncomfortable with all the physical contact of the bath if you help wash him.
   3. Being left with strangers is scary even for ordinary kids but suppose for an autistic kid and preschool where absolutely no one seems to understand him. Imagine how scary that must be? How would you expect him to react if you say left him with people who didn't speak english? Well in a way the people around him don't 'speak' his language either.
5. Let me emphasise it again. No matter how 'irrational' your sons behaviour seems to you it's very likely not. He has needs that defy your common sense but your common sense is not a measure for what's rational. Try to look for reasons behind his melodramatic outbursts I guarantee you they are there.
6. Normality is not something to be aspired to. You may yet see a day when you can be glad of the positive things our sons abnormality brings.

It’s possible she believes he is normal because she also is on the spectrum, and maybe her family. It can be a difficult thing to bring up if the person doesn’t believe there is anything wrong with them. Are the preschool OFSTED registered? They should have a member of staff trained in special educational needs (SEN) could you arrange a meeting to talk to them? They may have noticed something themselves

Your ex is in denial about your son. Possible narcissism, to boot. 

I despise those who deny their ex access to the kids, barring exceptional standards. 

You're draining all your energy and receiving nothing but negativity from those around you. You understand so much about your situation, about the gaslighting and invalidation you're receiving from your ex, you moved so you don't have support or anyone to talk to about your child, and you don't even have a specialist to talk to to validate your child's behavior to give a diagnosis.

Your ex and her family could possibly be on the autism spectrum as well, so they do not see your child's behavior as out of the ordinary, and it's a possibility that they know how to handle those situations, so your child does not have outbursts like that with them. Or maybe your child does have outbursts like that with them, but they don't see it as out of the ordinary, because maybe they were all like that when they were younger. But I'm not completely sure, this is just me speculating on the matter.

So does both parents need to agree before getting a child to see a specialist to be diagnosed, or can you just go there by yourself with your child? I think that it'll be good to have a diagnosis for your child, because if your child is supported, it'll in turn be easier on you. 

I think that bathing can be a very terrifying experience for a child, because the running water and echoing sounds very scary and stimulate a sense of danger. Children can hear higher frequencies than adults can, because adults lose their hearing with time, so things can sound different to a child. Also the tub can be quite massive from the perspective of a child which might cause fear, and also there's a level of vulnerability from bathing because there's no protection around the body. So maybe some music, toys, a video playing, or something fun, can make the experience of bathing better for the child. 

Also when your child goes to preschool, there's a natural fear of abandonment, they fear that their parent might never return for them, and if the parent is forcefully pushing the child away to be left somewhere and then leaving, it really causes that fear to intensify. Maybe comforting the child and explaining that you won't be long, give them a toy or a token that represents you and that you're with them, might give them some peace of mind and reassurance, I mean they still might not like you leaving, but at least they have something of yours to keep and feel better about.

It sounds like your needs are not being met and you seriously need support for yourself. It's understandable to feel resentful when your needs are not being met. Just remember that the problem isn't his behaviour, it's the lack of acknowledgement and support. With acknowledgement and support you would be able to cope with these issues. Any resentment you harbour towards him risks spilling out and damaging your relationship with him. Try to redirect your anger towards doing what you need to do to get your needs met, and place the blame on whatever and whoever is preventing you from accessing support, rather than on your son.

There are a few things confusing me it might be helpful to expand upon.

Firstly I'm just trying to understand what exactly is going on with him when staying with her family. Is he still having issues with meltdowns at their home that are simply being ignored or denied? Or is it that he is not having meltdowns when he is staying there? Do they also have to strongarm him to get him to attend pre-school? Is he having meltdowns at their house every time the bath is run? Is his behaviour completely different when staying at their house or does he behave the same way but they are denying that there is any issue?

Secondly what exactly has she done to prevent you from accessing any help? I can understand that it may be within her power to prevent you from getting him diagnosed and getting support for him but is there anything she can do to prevent you from getting other kinds of support for you such as counselling, finding a peer support group, or accessing advice?