Congratulations on your new baby! I had similar circs to a PP - self employed husband so no paternity leave and like you I had my then 2yo to look after at the same time. Lower your standards and do as little as possible while you recover - make sure your focus while your husbands at work is keeping the children safe and fed and yourself rested! He will have to do more when he comes home from work to take the pressure off you until you feel fully fit again which can take a few weeks.
I gave my 2yo lots of attention while the newborn slept, lots of snuggling, undivided attention. If your 2yo naps as well you sit your butt down with a drink and relax!
Walking does really help you recover, do you have a double pushchair? Once you feel ready it’s really nice to have a slow walk with the kids, it helps you feel better and breaks up the day. I’m lucky as we have a park a 5min walk away so maybe week 2 I’d take a slow walk down to the park, let toddler run around then a slow walk back.
As PP says easy quick foods for your toddler, bananas, toast, fish fingers etc just stick to the easy stuff for a few weeks.
With regards to tantrums as you say it’s normal but I found that being really consistent with discipline and lots of positive praise - getting stickers and huge fuss when he does something good really helped.
5 days in you feel tired and still weak but give it a few weeks or so you’ll be feeling so much better so extra iPad or TV tome for your toddler when you need a break is definitely Ok! You can do it, I managed and I never thought I would be able to!