Don't beat yourself up laluna. Most of us have been there too. :)
Short term : get the presents back (I hope you don't live on a busy thoroughfare!). If your kids are still awake, go and say sorry and give them a big hug. I don't think you need to say anything more than "I'm sorry I lost my temper. I really shouldn't have done that. I have got your presents back, because although you were naughty, you weren't that naughty. We can talk about it more later, but now you need to go to sleep. I love you". If they're asleep already, you can say this tomorrow.
Please don't leave them: one total angry-mum-meltdown in 6 or 11 years is not going to do them much harm, and they'll have forgotten all about it before very long; but they'd be devastated if you went.
Tomorrow: go and do something nice for you - something that will relax you, make you laugh and/or make you happy. You sound desperately stressed and I think you need a break. You won't get a chance once the kids break up, so get in there, quick! Talk to your DH. You need a conversation about how you get some more support: a regular break when he's home, and something like 'telephone back-up' when he's away. Ask your kids if they want to talk about what happened, but don't push it.
In a few days : Personally (and I think I'm probably going against the grain here) I wouldn't talk to them about their behaviour today/tomorrow, because I think that will be heard (however hard you try) as "You were bad, so I lost my temper and hit you", which is not what you want to say. If you leave your conversation about behaviour, rewards, sanctions, etc. for a few days (you could maybe introduce new 'holiday rules' on Friday) then you can keep the two issues separate - your stress management/support, and their behaviour - which is fairer, clearer and more useful. Other people have given lots of practical suggestions...
Good luck! :)