Well go to court and have child support enforced. Also tell him to meet you halfway.

It is unfortunate for girl that her BD can't be bothered to get his shit together.

That said, who moved away from whom? If your wife moved away, it is only reasonable that she does the transportation. 

And really? LOL It is eight hours of travel time per month. What is this "it doesn't feel like we have a home" nonsense? 

Do four hours and four hours, too and back and then pick up ?  If wife moved she the one who has to do transportation.  If Bio father moved, It’s up to him to do the transportation,

You can stay over night and make a weekend of it. Turning something bad into something nice.  DW has to go to court to get CS in forced. Make the state handle the CS collection.

Does your wife work?

Go to court and get an agreement.  If there isn't one in place now, let him know that he can come pick her up, or meet you halfway, until the order is decided on.  And that order will include child support.

Oh, and it's his daughter, not yours. It's your stepdaughter. Might help to stop thinking of him as some intrusion into "your daughter's" life and recognize him as the bio father. 

The reason I asked if your wife works is ...IF she does not to earn money outside the home you resent that YOU are fully supporting another couples child.  I would not blame you for being ticked off.

Is your wife court ordered to do the transportation?  If not  and if it's a large burden, don't do it.  If, on the other hand, your wife moved away and the father is unable to do it (doesn't own a car, perhaps), then if your wife wants her daughter to have a relationship with her father, she should drive the child.  Is there a need for you to go? If you don't like making two 4 hour drives once a month, let your wife do it. And if your wife wants CS  she should go to court and try to have it ordered and/or enforced.

Mitigating the responsibilities of the blended family opposition is rarely a good idea IMHO.  

In our case the SpermClan had long distance visitation.  5Wks summer, 1wk winter, 1wk spring.   The CO clearly stipulated that each party was responsible for transporting the kid to their location.  Your SO either needs to immediatly get out of the visitation transportation business, at least in the direction of delivering the Skid to his X, or... he needs to get back to court for an update to the CO stipulating that BM pick the kid up for visitation. That does potentially two things, it gets her involved and responsible for her own visitation with the kid, and it motivates her to agree to a mid point drop off and pick up point so that it minimizes the impact of kid visitation transport on your life.

There were several occassions during te 16+ years we lived under the Custody/Visitation/Support CO where the SpermClan refused visitation due to the cost of Skid travel to SpermLand. That was even when we split a round trip ticket with them both when someone had to travel with him and after he was old enough to travel as an unaccompanied minor.  We would upon occassion pay for their half of air travel when it had been a year or more.

Even when we covered the costs of their visitation travel we made it clear that they had to manage their visitation relationship with the Skid.

This is a message that our SO needs to clearly deliver to the opposition parent.  He steps up or .... he doesn't see the Skid.  That your SO volunteers to be his transportation bitch is a head scratcher for me.