Checked calendar, rearranged a delivery we had coming that would have clashed
• Responded to parent saying we were going, asked about an allergy issue
• Bought and wrapped present
• Got outfit ready
• Woke toddler early, went to park to tire out, basically forced early nap to make timings work
• Prepped toddler re. what would be happening, expectations etc
• Looked up directions and how long it would take to get there (never been to venue before)
• Packed bag, water, wipes etc
Fuck me. Your child went to a party. How on earth do you cope with something actually complicated like moving house if you make this much of a meal of things?
"Prepared toddler"
"Got outfit ready" Fucking hell
Can I ask if you have more DCs, and if you work? I do genuinely think you could make life a lot easier for yourself and also make yourself less stressed by overthinking what is basically simple every day life.
How many parties do you go to a year? If it's lots, perhaps buy a bulk load of little gifts and gift bags to save your time wrapping (and better for the environment). It may take 30 mins as an initial investment but saves time and stress. Things like books or art stuff are good? and stick the gift receipt in the bag. We always kept a bag ready ie took a minute to refill it after we had used it and just kept it in the hall ready to go.
Rearranging a delivery I agree is a pain in the arse but I take it that doesn't happen every time you have a party.
Checked calendar and responded, asked about allergy - perhaps a couple of texts, five mins?
Have presents ready as above
Got outfit ready and woke toddler - normal everyday stuff, perhaps nicer outfit than usual 
Went to park and napped - everyday thing except you made it a bit earlier.
Prepared toddler - just have a conversation in the car while your DH drove? No extra time out of the day required.
Looked up venue - one minute on Google maps.
Packed bag - have it ready as above.
No need for all the listing of onerous tasks as though it was a trip to Mount Everest.
Admittedly my DC are older but this actually took longer back then as it involved written invites and responses
and an A to Z, phones make everything so much quicker and easier! One of my DC had SN so arrangements were complicated - the downside of that was that they weren't invited to any parties. Being invited to a party is such a lovely thing for a DC, it's not worth complaining about stuff like having to get a bag ready FFS.
My DH was actually the SAHP at some points so did all this, if he had presented me with a list like that complaining about the mental load I would have laughed - and he wouldn't have done it as he had a sense of proportion! And as an adult I was interested in what was going on in DCs lives even if I was at work all day, I knew when their parties and parents evenings were, I could see when DH looked knackered and suggested he sat down while I did bedtime, I would think it was almost time for buying school uniform and we needed to get on it. If I was away/working late I'd ring him after bedtime and let him moan about parents evening 
We were, and are, are equal parents no matter who is doing the work at home and who is doing the work at work, and looked after each other as much as looking after the DC. It needs to be like this from the start. It's not some kind of unobtainable utopia, it's just setting out your stall and boundaries from the start.