It often happens that I’m travelling in hotels with my mother and sister.
I wake up earlier than they do in order to daven before zman kriat shema. However there’s a problem:
I find it very hard to daven with any sort of kavenah whatsoever davening in front of them. This is particularly a problem in smaller hotel rooms. I also don’t think it’s proper to daven in sight of women (mechitzah rule).
The only alternative would be to daven in the room’s toilet, but that’s assur.
So what should I do?
If there is a shul within reasonable distance, the most preferable option is to daven there, for there is a halachic preferance of davening in a shul even when there is no minyan present.
I understand from the question that there is no quiet room in the lobby of the hotels which can be used for prayer. If there would be, this might be an option.
Assuming neither of these options is available, you should daven in an area of the room that is away from your mother’s and sister’s beds, such as the area outside the bathroom. As you write, one may not daven in the bathroom.
The question of davening within sight of women is debated by Rav Moshe Feinstein, who rules that there is no halachic restriction of davening in sight of women, and the Satmar Rebbe (Divrei Yoel), who ruled strongly against the practice.
According to Rav Moshe, the halachah of a mechitzah (the obligatory partition between the men’s and women’s galleries) means to separate men from women, so that they should not intemingle and come to frivlolous behavior, but in principle, even a glass mechitzah would be permitted (though not recommended). According to the Satmar Rebbe, the purpose of a mechitzah is to prevent men from seeing women, for by seeing one another (and by means of thought) they would be considered intermingled.
In any case, to help you to have proper intent in your davening, you can face a wall, close your eyes, and try your best. Hashem doesn’t expect any more than that!