Of course you weren't wrong to ring your mum. It wasn't for a nice little chat, it was because she is a gatekeeper for medical advice, and as it happened, the one that gave you what you needed quickest.
I can't get over him sticking his middle finger up at you. It seems to epitomize his behaviour in a nutshell.
if my husband was at hospital with our child and got a lift back home with someone he’d shagged (assuming you did here) I would not be very happy at all. I would find it extremely disrespectful. Regardless of who does or does not drive I’d expect him to get a taxi and I’d afford him the same respect.
She didn't shag him. Mum, DP and OP don't drive. I don't know what other options DP thought she could pull up but I think it's much better to accept help from a friend who is right there than to waste time and potentially a lot of money calling a taxi. I don't know how far it is, but she'd have to get them to wait, on the meter, while she packed things or when she was done call and wait - away from her sick child. Perhaps you think it would still be necessary to spend a lot of money, use time and energy calling and waiting for taxis away from your sick kid out of respect for your DP... I would like to hope that my partner would be WAY more offended by me doing that than just accepting the lift.
The fact that OP did manage to produce another friend (a nice safe female one) who could come and give a lift, just goes to prove how resourceful she has been in this emergency. She has looked after an ill child, sought help deciding if it was an emergency, called 999 and told closest family, gone with child in ambulance, been with child in hospital, handled being worried about child, an upset and rude partner, and reassured child, arranged a lift, gone to pack, returned armed for an overnight stay. In that same time frame her partner has left work, got to hospital, and been rude and upsetting to somebody who is upset and doing all the legwork.
When the dust has settled he needs a metaphorical clip around the ear about the way he has treated you. He had no right. Yes he was upset. So were you. He should have handled feeling upset that you didn't call him first, much better. He should have handled feeling insecure about the friend much better. He should have, even if he was upset with you, recognised that this is a crisis and his hurties were nowhere near important in the grand scene of a very ill child. He should have been looking after you in the hospital just as you were looking after him. He should have been doing everything he fucking well could have done too have made the situation even a tiny bit more bearable. He did the opposites of those things.