I have nothing against hospital medicine. I thank the Lord above for hospitalists every time I have to send a patient to the hospital and don't have to admit them myself
That said, if you think you like both hospital medicine AND rheumatology I would think carefully about what it is that really attracts you to both. Both specialties are quite different in terms of clinical matter, day to day practice, and practice management. It would be more or less like trying to practice both rheumatology and gastroenterology--it would be very hard to keep up on current practice skills and research in both specialties concurrently, particularly if you have a busy practice. One of the glorious (to me) features of rheumatology is that I more or less never have to set foot in the hospital. I might get 1 or 2 consults a month, and even many of those probably could be handled over the phone with close outpatient follow-up; it will be slightly more than that with endocrine but only slightly. From a purely practical standpoint, you will have to maintain an outpatient practice for your rheum/endo practice, and it will have to be open even during the weeks you work as a hospitalist. So that will mean overhead (rent, bills, staff, etc) that you are paying out of your hospitalist revenues for those weeks you aren't generating revenue in your outpatient practice. This would be less of an issue if you were in academics, where your clinic overhead is shared with other providers and covered by the university physician group; I'm sure most university IM programs would be more than happy for someone to cover one of the ward teams for a week per month, or a month per quarter, or whatever.
If you just like both hospital medicine as well as outpatient medicine, I would give serious thought to finding a "traditional" inpatient-outpatient IM position. This will be more common in smaller/less-urban areas, but you could probably make it happen anywhere. I also know people who've worked several years in hospital medicine, gotten tired of the grind, then transitioned into an outpatient-only IM practice and are happy with that. Obviously some people transition back the other way as well. But as far as combining rheum or endo with hospitalist practice, while I think you could theoretically do it, it would be tough