I found out my ex was cheating for the second time, with the same woman .... and threw him out. It was like a lightbulb had gone on in my head at that moment and I knew I deserved better, and would never be able to trust him at all ..... trying to trust him the "first" time had been bad enough.
As for taking children to hotel room. Do you mean it was a room you had booked for yourselves, or, that you got an inkling he was up to no good, and tracked him down to this hotel ? Either way, not an ideal situation (kids wise) ....... BUT ..... I do sympathise tremendously and had I been in that self same situation I don't know what I would have done. If you're given a chance to catch an errant partner (who, if typical, has been giving you a load pf insulting bullshit, possibly telling you that you're going mad etc) but you have no one with whom to leave the kids, what do you do ? Some men will lie through their teeth again and again and again, despite things "feeling" very wrong (gut instinct) or, refuse, when asked directly to admit anything and put you out of your misery.
If Mrs TT was in a similar situation I feel that maybe she had no other choice ..... force a conclusion (of sorts) to the mess she was living in, even if the children had to bear witness (and I'll repeat, I know that's far from ideal) or carry on in a situation where she's made to feel mentally ill for "imagining" things.
Feel so sorry for you .... but there is life on the other side believe me.