Suggesting that a simple snotty nose is ruining a holiday is a bit disingenuous. But let's break it down a bit anyway.
If the op's kids are anything like mine then it's not just a snotty nose. A cold lasts several days, and comes with a snotty nose with constant sneezing, which has to be wiped endlessly, leading to sore facial skin, which makes her iritable and grumpy. When she sneezes she launches snot across the table, and she's two, so asking her to put her hand over her face or use a tissue is hit and miss at best. Who wants to have that in a restaurant or indoor event? Or at a soft play or whatever? It's a surefire way to spread germs, and as much as I love kids, I don't want other people's kids snotting on me, and I'm sure everyone else feels the same about mine.
On top of that if she's got a simple cold then she's miserable, lethargic, grumpy, clingy, cries a lot, whinges, has no tolerance or resiliance, doesn't want to play or eat or do anything except sit on my lap and cuddle. Making it very difficult for me to do anything. And making the atmosphere unpleasant for others around us. Finally it feels pretty cruel to try and make her join in with any social event whether it's child or adult focused. She just wants to be home, where she can be in comfort and nap if she needs to.
I have elderly parents with health concerns that make them vulnerable, so visiting them when dd is sick is not an option, as a simple cold could make my mum quite ill, so that's most family events out when dd is sick. And we can't send the kids to them for childcare when sick either.
And that's just if she has a cold. It's rarely just a cold. If she has diarrhoea, and she's had that about 8 times this year, she needs to stay by a toilet, and she needs someone to help her, so no long car trips, definitely no flights, which absolutely screws up family holidays. And no working for one parent. Same with vomiting. And if she gets a high enough temp she often throws up. Which means a 48 hour exclusion from nursery, even if she's fine the next day. Which means taking more time off work (which me and DH do share equally, but still it's a problem).
Until recently a temp or a cough meant a PCR test, with a minimum 24 hour turn around, so she'd be home for a day and a half at least, even if it wasn't covid. The time she got covid she was off for a week, and then her brother was off for a week. Not the same week, mind, he was the following week. So two weeks that DH and I had to juggle childcare, and then we got it too.
It feels cathartic to get this all down, but the reality is it's a fucking nightmare. I'm starting a new job in a couple of weeks, and I am so worried that I'm going to end up having problems because I have to take time off sick or to care for the kids. I don't know what the solution is either. I don't want to move dd from her nursery setting because when she is there she absolutely thrives, and the setting is perfect for her. I don't think she would be as happy with a childminder and she would definitely be lonely at home with a nanny. I cannot give up work, I simply can't afford to do that. I do work from home, and i have worked around the kids being home sick sometimes, if it's just one, then it's do-able for a couple of hours. But it's not possible with 2 under 5, and it's not possible for more than a few hours, I end up being a poor employee and a poor mother. Can't send the kids to my parents. Dh's parents are dead, so that's not an option. My siblings work full time and live 40 minutes away, DH's sibling lives 2 hours away. So no help there. Not sure what the answer is really, i just hope it gets easier eventually.