Oh dear, my apologies. I had typed this up and was sure I had posted it as well. I clearly didn’t. So here is my summary, in case it's of use for someone. And thanks for everyone’s suggestions on this thread, the trip was a success. To recap: we had 4 full days, 5 nights, in an apartment near Denfert Rochereau (so metro travel required nearly every day), 2 adults and 2 kids DD1 was 12 and DD2 was 9.
We went in the second week of April, just before Easter. Most of the fountains were still dry, to everyone’s disappointment.
We just bought metro tickets as ‘carnet’ and again for us that was the simplest and cheaper than travel cards aimed at visitors, as in general we just did one journey in the morning and one back in the afternoon. Note that you can only buy child tickets as carnets of 10 not as singles (as I was trying to do when we needed just a couple more on the last day). But apart from that, the ticket machines are very easy to use and take credit cards etc. In some Metro stations there is an awful lot of walking between platforms, just like in London, with stairs everywhere, escalators seem less common.
We did buy the Paris Museum Pass (museums only) - bought them on arrival from the tourist information kiosk at the gare du nord. You manually write in the start date, so we started them from the next day. They got us into the priority queues and I had superficially totalled up the costs of the the things we might have visited (max one museum a day) to judge whether it would be worth it, in the end the 4-day ticket cost €62 and on the door that would have cost us more like €113. Children go free.
So, yes there were security checks everywhere, even most big shops and all shopping centres had guards on the door to do a cursory bag check. At the museums there were always priority queues for ticket holders, great for us, but we were prepared and carried books / stuff to pass the time anyway. The worst queue was the Louvre, some places had hardly any or none (Musee D’orsay, Centre Pompidou).
For the Eiffel Tower you queue twice, first to get inside the security perimeter under the tower itself. That was really well organised with lots of ‘gates’ and it moved fast. Then you had to queue for the lift/stairs. We did the stairs, that still took 15/20 mins queueing. The stairs itself are totally manageable, my 9 year old skipped to the top and we saw plenty of younger kids. The second level of the Tower was massively crowded (with people queueing for the lift down or up to the third level) and DD1 got a bit distressed so we went down quite quickly again.
To get back home from there we had to take the Metro 6 - it goes overground for quite a while, including crossing the Seine and was a lovely ride.
In terms of apps etc: the Louvre app sort of worked to find my way to specific paintings we wanted to see. Another app that worked well to plan your travel on public transport is 'Next stop paris' by RATP.
In April the Centre Pompidou was still half-closed post-refurbishment, so a whole floor was closed and the pop art I had promised DD1 did not materialise. But DD2 enjoyed some of the installations and the Matisse paintings she recognised from school lessons.
Slightly off the beaten track, we all enjoyed the Musée des Plans Reliefs, it’s on the top floor of the Musée de l'Armee, a collection of models of fortified cities made in the 17th(?) century for military purposes. And if you’ve already seen all the big attractions, an interesting if somewhat mixed and varied museum is the Musee du Quai Branly. An Ethnographic collection from all corners of the globe. It has a cool art installation in the entrance, a ‘river or words’ that flows down the internal access ramp, DD2 and I had fun spotting words floating by.
Another Interesting thing was the crypt of Notre Dame, tucked away in one corner of the large space outside the cathedra. Itl has some interesting background on the development of the area, and some cool interactive screen-based exhibits to explore the cathedral building. We did not queue for the towers but went into the church, that was another fast-moving queue). Round the corner from there i sainte chapelle, that is a gorgeous building, not too busy and DD2 and I had fun examining the tiled floor in great detail - it has many animals depicted.
Amorino ice cream was a total hit. We didn't get the chance to try the Bouillon-Chartier as DD1 was happier eating at ‘home’ after having to endure crowds all day, but everyone enjoyed our outing to a local creperie on the first evening.
For a bit of fresh air, the play area (small fee) in Luxembourg Gardens was a great success with the 9 year old. It seems to be in two halves - one aimed at smaller pre-school kids and one with larger climbing frames and a superb zipwire aimed at older primary kids. Us adults sat around the perimeter where there were plenty of benches.
Travelling by Eurostar was easy and comfortable, although the departure lounge in Paris was being rebuilt/refurbished and only had a fraction of the required seats so we all sat on the floor. It may well be completed now.
And right after coming home I wanted to go again. Maybe without DD1 though, she would have been happier at home but I had no idea: she had never really engaged with the trip, until the first evening in Paris when she broke down in tears telling me how much she hated it, but that’s for a different discussion (HFASD/Aspergers).