You need to understand that in Paris the hotel rooms, unless you are staying in a luxury hotel, are typically going to be on the smallish side. So bringing in additional twin beds for your aunt and Dad to make 2 double beds for each of them is likely not going to work in a standard room that is outfitted with just 2 twin beds.
Consider staying in a hotel or apartment rental in one of the double digit Arrondissements that has good connections via public transit, or just get yourself the Uber app when you want to get someplace in the 1st-9th Arron and don't feel like walking or taking public transit. It's really not that expensive when you are splitting the cost among 4 adults and you are getting door to door service vs. having to find a taxi stand. Uber has a fare estimator tool so you can see the price - for example, a ride from the 10th Arron to the Eiffel Tower is about 16 to 22 Euro on Uber.
I stayed at the Ibis Gare du Nord Chateau Landon once in the 10th during the month of August and landed a really great deal online. I loved the 10th. The hotel was within walking distance to Gare du Nord and Gare de l'Est, multiple Metro lines, the RER and several bus lines. The hotel room had A/C, there was an elevator (handy if you are traveling with older relatives). I declined the hotel breakfast and opted to walk to any of a half dozen bakeries in the morning to grab something on the go along with a coffee - never spent more than 2-3 Euro total. That part of the 10th was a good mix of working families (blue collar and white collar) and young professionals. Lots of reasonably priced restaurants, groceries, delis and shopping nearby.
Although Citadines and other apart'hotels are great options, you can find other reputable apartment rental agencies if you are not wanting to gamble with whether your Airbnb choice is legal or the owner might decide to cancel your reservation to take on someone else who wants the place for a week or more. If you do a search of this board, you'll find the names of a number of agencies people have used for apartment rentals, but again, Paris apartments can be small and it's next to impossible to find one with central a/c or multiple a/c units.
To give you an idea, we rented a 3 BR 1.5 BA in the Marais last summer and spent around $425/night to sleep 3 adults and 2 older teens. Sure it's a single digit arrondissement, but we still had to walk anywhere from 5 to 10 minutes to get to the Metro depending what line we needed, or else we took an Uber. The building had an elevator (also rare to find in older Paris buildings), but it was the size of a phone booth. To get up to the 4th Floor where our rental was, only 2 or 3 of us could get in the elevator at one time (that was without any luggage). We did have an air conditioner, but only in the living room. Luckily for us, there was only 1 or 2 days where we needed to turn the A/C on and the temps dropped a lot after the sun went down - there were also ceiling fans or a pedestal fan in every bedroom. There is no way one A/C unit would have sufficiently cooled down the back half of the apartment where 2 of the bedrooms and the full bathroom were located. There was only one queen sized bed in the master bedroom. The other 2 bedrooms had twin beds, but they were bunk beds because the bedrooms were very narrow. The official check-in time was not until 3PM and the owner had said he would not let us in earlier but would be willing to hold our luggage provided he was on-site before 3PM. We had to pay a security deposit (refundable) and a non-refundable cleaning fee in advance. We knew all of this going into the rental, so there were no surprises for us, but for some people these things might put a damper on renting and make a budget/business class hotel a lot more appealing.
