He definitely is trying to screw her over.
He gets £47,000 a year, which OP says is the "higher" of the wages. He's asking for 50:50 on paper but is not able to do more than 2/3 "nights" a week (after 8.30pm). He wants half the DLA and the motability car and be listed as the primary carer so he receives the UC element.
So he would get £47,000 + £2,870.40 (half DLA) plus UC top up and motability car for 8.30pm - 9am care maximum 3x a week (37.5 hours, most of which they'll be asleep) plus, let's be generous and assume one of those days is a weekend (+ another 12 daytime hours = 49.5 hours a school week). Fuck knows what his plan is for holidays, illness, insets...
In ex's scenario OP would get a lower wage (£25,000? £35,000? £40,000?) + £2,870.40, no UC top up, no car and the mobility component DLA tied up in the car the ex is driving to work. She would care for at least the youngest child 3pm - 8.30pm on the ex's nights (severely impacting her ability to work). Assuming she also has a weekend day, and taking into account school, she'll be doing over 80 hours a week caring, for a lot less money.
If he really, truly wants 50:50 (which is extremely unlikely to be beneficial for the kids), he needs to do full days and nights, half of weekends, half of holidays. The motability car needs to be given up and the component claimed, then all the DLA split in half exactly. UC should then see who is entitled to what, if anything, in the separate households (salary + £4,873.70 DLA both components + any UC they are separately entitled to).