The only campground inside the park with hookups is Fishing Bridge. IIRC, sites are up to 40’, cost is about $50 per night. Sites are double width so you could theoretically park the trailer next to your RV, but it would be a tight fit, probably couldn't extend slides, and would still need a place to park the jeep.
So looks like you need to stay outside the park.
By the way, you probably know from the NPS website that - contrary to an earlier post, - the campgrounds inside the park are NOT twice the cost of others outside. Most are about $25 or less, and all except Fishing Bridge give a 50% discount for senior pass holders.
It is also not correct that only two in the park take reservations. Several more do, all through Xanterra, the concessioner. The NPS has another batch that are first come-first serve, no hookups. The one than can handle the longest rigs is Mammoth near the North Entrance. Mammoth entrance and campground are the only ones open all year.