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Gutmutter, I hate to say it, but your brother is misinformed. You can easily get accommodations in Yellowstone at any of the hotels, just maybe not in July. I had rather go in mid August to September (elk bugling!) or late May/early to mid June when all the baby animals are new, anyway. Besides, the crowds are FAR less at those times and big crowds ruin the national parks for me; plus your daughter will be at her busiest then. August normally has lots of openings too. If you are not hell bent on a certain date or type of room, you can go.
Even the "Frontier cabins" at Lake are an option, within an easy walk of the hotel. I've stayed in those and as I remember they were nearly $100 less than the least expensive hotel room. And they are not really what I and I suspect you would call 'frontier', unless that means "no TV" to you. They are more like "teeny tiny houses". When you check, go to
Yellowstone Cabins, Accommodation, Inn, Lodging, Camping: Xanterra. which is the official site, do not go through other avenues or you will get ripped off. Make sure when you view the dates, click through all room types as they all won't show at once.
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you know I am a travel nut; I just had to look and almost all days in August and even a good many days in yucky-to-me July have openings in the hotel itself for "standard one queen" and even lakeside rooms. There are also the little cabins available. Don't make the mistake of having less than 3 whole days there and obviously more would be better.(The little cabin does have 2 beds, and would even be cheaper if you wanted to go in the last half of August with a very good, experienced, and knowledgable but inexpensive driver and guide to take you around the park for some or all of your days...

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If you want any help planning your Yellowstone trip, PM me and I'll help--even could let you have my phone #. I KNOW you would love to go out there, even if your daughter were not working there which is a huge bonus.
In my own good news, I just got back from Tijuana, and I left half my stomach there; I am having no pain, and am looking forward to getting healthier.