Would you go to the funeral?

DH is from a huge family, both sides, particularly older generation so there have always been lots of funerals.
He likes to go, it’s not always possible as it’s 4 hours each way. I had to tell him to stop comparing himself to people who are ducking out of work for a few hours to him having to travel/hotel/use annual leave.
I think if he go and wants to and is able, fine. If it’s difficult then probably not.

@Witchonenowbob OP says they (as in her and DH) don’t have a close relationship with SIL and BIL

It’s very normal for some people. There’s no right or wrong. But I would think your SIL invited him because she could do with her brother’s support.

I see you've settled your dilemma re the funeral but I find it odd you talk about 'we' regarding a relationship with his sister - surely he has his own relationship with her independent of you.

OP has confirmed she doesn’t like them, she hasn’t confirmed how her DH feels or if he wants to build bridges.

My brother, mother and I went to my BIL's father funeral. My brother and I had never met him, but our attendance was very appreciated by my sister and BIL.

Sounds like your SIL has explicitly invited your husband so he should go.

I am not English and I find the attitude surrounding funerals in England very odd. If my DH wanted to go to a funeral, no matter how tenuous the connection, I would definitely do whatever I could to help him get there.

He actually went to a funeral abroad last year, of an old school friend he hadn't seen in ages. He would have taken a very dim view had I called it a waste of annual leave.

Yes agreed. But if you don’t like the friends and family attending then there’s no need to go support them.

The funeral is about supporting the bereaved, not the dead person.

You seem to be backtracking from your original premise which was that you wanted to be able to tell DH he can’t go to the funeral. I think you have accepted that you can’t do that.

However, you can say he can’t borrow your car to go if you need it. He can get public transport and get collected at the other end surely?

That’s what you think, what does your DH think?

A) I can see why his sister would want him there, it’s probably more about supporting her and her husband rather than the relationship with the deceased.

B) Yes you would be very unreasonable to say “don’t go” it’s not your decision.

YABU, it's up to him. You don't have to go

Funerals are for the living. If your DH is close to his BIL it would be the right thing for him to attend to offer condolences and support.

Can't he get the train there, or close enough on the train and then a taxi?

I think this is key. You don’t have to rely on your judgement about what the right thing to do is - you follow the lead of the person bereaved.
A friend recently lost both her parents within a week of each other. I knew people who had been their neighbours and let them know. They asked if they could go to the funeral and my friend wanted to check how her sister would feel. Some people are very private in their grief and it feels like you fall into that kind of response. As you can see on here, other people feel they really need the support of others and that people coming to a funeral of their loved one is an open acknowledgement of their loss and grief.
Your husband could always say to your sister “would you like me to be there? How can I support you both?” Then there’s no second guessing. I suspect she will want him there - otherwise she wouldn’t have asked him in the first place

And they've asked for him

When my mum died there were plenty of my friends who didn't really know her.

They were there to support me.
I'm struggling to see how you can't see this.

But as your DH has been invited, presumably his BIL doesn't consider him a random and wants to have him there.

And surely support is important not just at the funeral. If you are not close to SIL and BIL, I assume not much support will be forthcoming (or required) at other times.

DH and I didn't got to his brother's FIL's funeral. It was in a different country and we had never met him. No expectation of us going.

Not sure whether there would be any for us attending the MIL's funeral whenever that happens (in good health at the moment). Only met her once at their wedding. Ginormous family on that side of the family so would not need additional support from us on the day

Kindness. Because it sounds like his sister is asking him to be there.
Funerals are as much about those bereaved (if they want and need the support) as those who have passed.
I recently went to the funeral of my friend’s dad. I’d met him fewer times than you’ve met your BIL’s mother but the funeral was going to be tricky for many reasons and my friend needed the support.
I also attended the funeral of another friend’s mother who I had never actually met. In fact I went to do the food for the wake and to generally help her out. And again, she wanted the support.
If she’s asked him and he doesn’t go, people remember who doesn’t put themselves out. If relationships are sketchy, it’s an opportunity for a reset. Unless they’d done sth unforgivable, or I had an unsurmountable clash, if I were your husband I’d probably go in these circumstances.