Or is he, RE splinter in child’s hand?

[Pettyspaghetti]

Looking for advice on this, and if I’ve gone about it the wrong way.
DD (5) showed me a splinter that she gotten yesterday (I work nights so was at work when this happened). I asked DH why he hadn’t removed it, to which he replied “she would let me”.
I asked DD if I could have a look and take it out. She refused. I tried reasoning with her, telling her it would get very poorly if left in etc but she wouldn’t let me anywhere near it. So I left it, and told her we’d have to get it out after school.
3pm comes, and once DD is home from school and settled, I tell her that we’re going to get the splinter out now so it won’t hurt her anymore, and possibly get infected. I tried numbing it with some ice first, and attempted to take it out. ALL HELL BROKE LOOSE. DD turned into some sort of demon, kicking, screaming, the works. I’d barely been able to touch the bloody splinter! While I’m trying to wrestle with the banshee in the kitchen, DH is sat on his phone in the living room, completely ignoring the issue.
I eventually gave up, my ear drums were close to bursting and DD wasn’t cooperating. I turned around to see DH watching me with a look of disgust on his face.
I’m now at work, and have since had a few messages from DH saying that I was wrong to try and remove it, and that I have traumatised DD . He’s made me feel like absolute shit! I know splinters aren’t pleasant, but the alternative is an infected hand which would be much worse. DH has very blatantly put the blame on me, and now I’m a rubbish mother (according to him)
Was I unreasonable in trying to remove a splinter from my daughter? Am I being too harsh on her?

To be fair, my divorced parents had to reunite, step parents in tow as a kid because it took four people to get my eye drops into me for my frequent conjunctivitis. I think that's what it was anyway. Splinters never came out, we didn't have enough parents for that 😂😂 and I still can't stand to cut my nails. My husband has to do it, there's a whole ritual. It must be so upsetting as a parent though! I hope she feels better soon!

I think I’m married to the same man. Letting them do stuff as far as possible works here. And sweet bribes.

Not all work their way out and many are painful while they're in. And there's an obvious risk it'll get infected.

I've had to do 3 in the last couple of weeks. Haven't had to do anything fancy yet. I just have someone cuddle DD with her arm behind their back and use a pin to follow the splinter in and pull the end out. Then I use my nails or tweezers to grab the end. She doesn't particularly enjoy it but it's the quickest and cleanest way to get them out.

I'll definitely remember the syringe trick for if she gets a worse one though. I don't 'dig' with the needle and any tricks to avoid it are very welcome