It sounds to me like the contact order needs varying (assuming that there is one) - the DH and XW, when she moved, should have immediately gone back to court with a request to vary the contact order - the entire concept of weekday contact is unfortunately an unworkable one with these distances - especially if their own father can't be arsed to be in the driving seat (literally) of making it work. It's also really unfair on the little boy having to go back and forth in the middle of the week like that because neither his actual mum or or is actual dad have a shred of responsibility to vary the order. They don't even have to go back to court (in reality) - all they needed to do was have a conversation, say it's not going to work let's move to weekends, job done. The court wouldn't care where all parties are happy but if they want to formalise it, it's back to court.
And don't bash the XW for moving - you have no information on her reasons - they could be entirely thoughtless to the ramifications for everyone else including her son, but there may be really good reasons too that none of us on here have a clue about. When I divorced I moved 80 miles away in a north-westerly direction in order to be able to afford the required 3 bed house that I couldn't afford in the same town we'd been living in, secondly whilst living in the original town their D'F' despite being only 10 minutes away did not see them EOW and one night in the week picking up from and dropping back to school as was put forward as the interim arrangement by solicitors, no, he saw them from 11am on a Sat to 4pm on a Sunday and in fact once he'd taken me to court for contact (!!) that's when they started seeing him more!! I wasn't taking my children away from an established and enthusiastically engaged with contact regime - we didn't have one because their dad is a [insert word of choice selfish bell-end].
However, in acknowledgement of how far I had moved (a 45 minute trip each way on a good day) and how much I wanted my children to have regular contact with their dad, I, as the children's mother and the one who had moved, ensured that we met half way at the 45 minute journey point at all times - so it was fair. And can I say that their SM was not involved, never did a drop off or pick up and we did that regime for 8 YEARS. And she didn't do it and it never even crossed my mind, because it's NOTHING TO DO WITH HER! It's not the stepmum's responsibility.
OP - you sound like you are doing SO so well with your DSS. I only wish that once my XHs wife had had her baby she hadn't completely gone loopy and started being really quite horrible to my children such that my DD only sees her dad about 3 times a year because he's not 'allowed' to come up here and see her. The way that you have deliberately set out to treat your DSS the same as your other children - I take my hat off to you and truly believe this is the only way to approach it and definitely the only way with children of this age where you have opportunity to create an additional ell-functioning family unit. Good for you, it makes my heart sing that you have this attitude. That little boy couldn't be luckier to have you 
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But.
Whilst you can indeed help with transportation for contact it's not actually your responsibility. Your DH has been, actually, completely irresponsible. In fact, he's treating you and his own DS appallingly when you look at it. He'd be happy, potentially, for his DS to be left at the school gate rather than communicate with you OP, in order to make other arrangements. He should never have expected you to do the journey - shame on him for that; and he should be ashamed, that assumption was appalling.
You stick up for yourself OP - it's not being a bad stepmum in fact it's quite the opposite, especially where you're so incredibly tired and it could be dangerous. It's not deferring to the new baby over DSS, it's acknowledging that a newborn needs an incredible amount of care and that includes the ability to frequently directly observe them which you can't do when they're strapped in a car seat for two hours.
Also, I hear what you're saying about city centre traffic in the city you referred to - my 10 mile journey home from the city centre can take 50 minutes when the schools are out, but anything up to 1.5 hours the rest of the time for what should be a 40 minute run! And 'pulling over for a rest' or 'pulling over to check on the baby' wouldn't be an option on the main routes - you'd either be on a fast moving dual carriageway or a main A road and would literally hold up everyone behind you and cause a major traffic jam. And any journey where in order to complete it you're required to pull over several times to check your occupants are still alright, is a journey you shouldn't be making in the first place.