Given that many MPs have to spend a minimum of five nights a week in London for very many weeks of the year when Parliament is in session, the level of MP expenses/allowances you are proposing would deter all but the very wealthy from standing for Parliament, and certainly very many mothers. Can you really expect fairly ordinary parents in particular to sleep at a Travelodge or whatever for months on end with brief visits at home at the weekend if they are lucky, never seeing their kids ? Like some sort of Open Prison arrangement? I for one wouldn't ever dream of standing for election if that was the deal, until I was so past it that I was a lot less use than I might have been in my prime. No sane person would.
It's entirely different in the Armed Forces as you do a few carefully planned tours of duty and then retire at 40 or whatever, or move to a desk job, so it doesn't need to be as sustainable. They is also barracks for accommodation and mutual support for Army spouses and children, so families are not marooned and trying to sort everything out for themselves at a distance, like MPs' families.
There is also the matter of first class travel. For anyone who has had a demanding job that never ends, like being an MP, and who has to travel regularly and endlessly for work, there is a direct correlation to the amount of extra paperwork and emails you can get done in a week and the ability to park yourself somewhere with a table, a socket, wi-fi, and fewer leisure travellers. It's perfectly reasonable for them to do this, especially if these are long inter-city trips, and if people on here had had more experience of this personally I think they'd be a lot more sympathetic instead of fixating on the apparent status aspects of paying extra for these facilities. All you get in first class is what is standard in lots of other countries, and on Eurostar. It certainly isn't champagne all the way, no siree.