Hi Ka-mon
Levemir is a long acting insulin and essentially has a slow release, so it comes on slowly and lasts for a long time. As the others have said, basal insulins are supposed to deal with the daily trickle of glucose coming from the liver, not the spikes that come from food. Because of that, it shouldn't make any difference when in the day you take it as in theory it lasts all day long (although most find levemir works best split into two doses). If you do split it, then the doses are supposed to be 12hrs apart. I haven't heard of anyone saying take your background at times to follow your meals before. Because it's 12 hrs apart, you're really left with early-mid morning and early to mid / late evening depending on when you get up and go to bed.
IMO the hypos in the morning would be more likely to be caused by the amount of the 10pm levemir. You usually start with a 50:50 split with levemir, but I think lots of people change the split. For example, I take 3u am and 12u pm. I guess her pm levemir is too much and her am not enough, but that's only my view. I dropped my am dose because I was going hypo before lunchtime and again before tea. However I'm still a little high in the mornings, hence the 20:80 split.
My guess is that when the doc says four injections, he means a multiple daily injection routine, i.e. Apidra / novorapid plus levemir (basal / bolus). I could be wrong but that would be my guess. That way your mother will get some insulin to cover the meals as well as the basal rate