Have been to Chaco many times but not recently. Great place to go, well worth the effort.
I've tent camped a dozen times or so and took a towable in one time. Would not take my MH in at all.The road in is bad. You cannot find a speed that will allow you to manage the washboard. During rainy season, late summer, I think, road is slicker than any ice you have seen. One wet crossing is 3-4' deep after heavy rain.
Bloomfield parks are not good. Would Farmington or Aztec be better? I have no experience. There are decent motels in Bloomfield. Best place to park MH in area, in my opinion, is 40 mins east of Bloomfield at Abe's Motel and Fly Shop, below Navaho Dam. Not beautiful but cheap and safe and world's greatest flyfishing for trout.
Another alternative is stay in Grants and come to Chaco from the south. It is slightly farther than from Bloomfield but RV parks may offer better options. Again I have no experience staying in Grants.
Let me know if I can help.
Good luck, work it out, it;'s a great place.