This whole bloody thing is nonsensical - makes me really angry to think of you doing that long drive when heavily pregnant. Even if you're lucky enough not to be suffering from backache, hip-ache, tiredness, or any other symptom commonly associated with late pregnancy, I'd feel wary about being 2 hours away from home - and with a car full of kids to boot - just in case I went into early labour.
The fact you've put all those concerns aside and have continued to do this massive favour should be commended, not criticised, and that SIL should f* off. I would love you to tell her in no uncertain terms how this is absolutely none of her business but appreciate that may not help family relations, so in the meantime, perhaps you should block her on your phone/email so you don't get to see her drivel directly. DP should be protecting you from anything that comes via him - and he should be telling her to butt out. Right now, you should be winding down, relaxing when you can in anticipation of the baby arriving - not worrying about all this crap.
The ONLY option is the train. If SD doesn't want to lower herself to travel on public transport then so be it. She probably has picked up on her mother and aunt's views, but is being ridiculous and should be ignored as much as possible. In other words, DP should reiterate this is the only way contact will happen - and reinforce the benefits of train travel, but I hope he's not tempted to bribe her to get on the train (start of slippery slope). He may have to resign himself to a few weeks of no contact - but chances are she'll back down when she sees DP means business, and no, her stropping isn't a way to take advantage of the situation. It's such a stupid objection ...... on a train she'd be spending more time with her dad (as Random points out), it's arguably more comfortable, you can sit face to face and talk properly without the driver having to concentrate on the road, there's a loo (!), it'd be her dad and not you collecting her etc etc.
Okay, DP can't drag her onto a train, but if his ex was also insisting she had to go (or else there'd be consequences) then there probably wouldn't be a problem. Ex is probably chancing her arm one last time, though what difference it makes to her whether the kids go in the car or on the train I don't know. Can only speak from personal experience of DP's ex raising pointless and shit-stirring objections and conclude that her attitude is based on spite - quite possibly there may be some jealousy about her ex having another child, and this whole "must be driven" business is one way of making things uncomfortable and awkward for the OP. Whatever - you are NOT to drive again, and the train is the only way. As I think I said before, if things escalate and SD refuses the train long term, then your DP should apply for a contact order with the aim of the ex co-operating to ensure SD sees her dad - can't think any judge would think it unreasonable for a 12 year old child to travel by train when there's no alternative and dad can't drive (for good reason).
(My DP used to get - in relation to contact - "I can't force them to get in your car" .... when there was no good reason for them not to, yet wouldn't attempt to persuade them in any way shape or form - be it reminding them that they'd have a good time at dad's (heaven forbid) or threatening them with a consequence if they didn't. She just used to go along with whatever the children "wanted". I always used to compare this attitude to what she'd have done had they announced they weren't going to school, or to the dentist, and am convinced that she, along with most parents, would have adopted either the positive reinforcement or the consequential approach - or a mixture of both. There's no way she'd have just stood there and gone "oh, okay then, mummy won't force you". Clearly, women like her don't value the father-child relationship and/or are so hell bent on upsetting their ex that they don't see the harm that's being done to their kids (by giving them inappropriate levels of power and by preventing the father-child relationship). Hopefully, your DP's ex is one of those who values her free time - she might become more persuasive/insistent with SD when she realises her social life's affected if the train isn't used!)