Firstly, I'd check if you your DD actually knows all the letter sounds (not letter names). Can she name them quickly or does she have to think about them for a moment or two? If she doesn't know them really well, it's going to be difficult for her to spell whole words. If she is writing letters the wrong way round, I would say it is very likely that she just hasn't learned them properly yet. This would be absolutely the first place to start. She really needs to look at a letter and say immediately what it is. The school should be able to give you some ideas how to get her to learn them really thoroughly.
Secondly, see if she can orally break words down into their sounds. You do not need to show her a word written down to do this. For example, see if she can break down simple consonant-vowel-consonant words such as cat, log, man, nap etc. Give her an example so she knows what you mean. E.g. "The sounds in cat are c-a-t. Listen, cat c-a-t. Can you tell me the sounds in log". If she can do three letter words, see if she can do regular four letter words e.g. lend, hand, song, flip, pens etc. If she can do four letter words, see if she can do regular five letter words e.g. flint, crisp etc. Your DD will need to be identify sounds in words if she is going to use "sounding out" to help her spell. If she can't do this, she needs to learn. Go and talk to the school about how she can be helped. It is a skill that can be taught.
Thirdly, see if she can read the words she is being asked to spell. If she can't, she really needs to be given other, more appropriate, words. Otherwise it is a pretty pointless exercise. Again, go and talk to the school.
Look, say, cover, write, check can work well but I would really recommend doing the little investigations I've suggested.
If given 10 (appropriate - must be appropriate - words) to learn a week, on day one learn two words. On day two, recap over the two words and learn one or two new word. On day three, recap the three / four words already learned and add one or two more etc. Only add new words if you DD can spell the ones she has already learned. Keep going over them every day.
Good luck with it all.