She is bullying you and forcing the issue by sending you the cheque, hoping that you will back down and do as she wants.
If you don't cash the cheque - or indeed, acknowledge receipt of the cheque - then you can pretend that you haven't received it and carry on making plans for her that don't involve lots of driving for your DH. It's up to you to decide how late the letter arrives (if at all!) - just occasionally the bad reputation that the Post Office has can be used to your advantage .
Would a train be very much more expensive than the cost of the petrol? Especially the way that petrol seems to cost a lot more than it used to - can you book an advance train or coach, they are often much cheaper if you can sort them out well in advance. And being cheekiy - and has she actually sent enough to cover the full 600 miles, not to mention wear and tear on your car? Does she realise the actual cost - both monetarily and the physical effort involved in doing such long drives, especially with the pressures involved on such a weekend?
Or ring up a couple of local (to her and you in case there is a difference) taxi companies to see how much they would charge to do the trip - even if they only did one of the trips it would save your DH a lot of driving on a weekend that he should really be at home for all the preparations / celebrations / tidying up after / etc of his DS's baptism. You could even be really brave and google lift sharing / share a ride etc and see if you could find her a lift that way!
And if you know that you will 'never hear the end of it' if you sort out a train ride/whatever for her, you and DH work out a strategy for dealing with it in advance, so that every time she starts to mention it you have got your counter statement that you can come out with (eg 'Well at least it meant that you and DH could actually be at the service with no trouble and that DH was awake for his own DS baptism yadda yadda...') - turn it into a game, the first one that gets to say the line to her 10/20/whatever/whenever times gets large choc bar/bottle of wine/shopping trip/cuddly toy/blankety blank chequebook and pen as a reward .
Good luck - hope you get to enjoy your special weekend together without turning into a long distance taxi service!