Oh Joanne I really really feel for you.
At the end of the day I can only tell you facts, I can't tell you what you want to hear. I would love to be able to say that your little boy will be fine on mixed insulins and everything will be hunky dorey but I can't. I'm sorry.
I don't know how old William is but again unfortunately that is irrelevant, it would just help me give you some tips thats all, my daughter was 5 weeks old when she had her first injection so we've done, baby, toddler, terrible 2, 3, 4 etc up to 9 1/2 years so understand.
I can tell you that mixed insulins generally do not work. I know probably 300 plus people who are diabetic the majority are children, the only other ones I know are on this forum. I only know out of those children two that mixes work for and we have no idea why. Everyone one has to, at some stage move to MDI (multiple daily injections) or a pump.
To get any semblance of control on injections you need to be able to match the insulin to what is eaten. On mixes you are chasing the insulin and have to give enough food to cover the insulin but because they are mixed you will not get it right at some parts of the day which is what you are finding.
With MDI you do not have any mixed insulins at all. The three insulins you have listed are mixes. You cannot possibly know what is happening overnight on mixes either unless you pretty much test hourly ! My daughter was on Mixtard 30 for a few months and was given a CGMS (continuous glucose monitoring system) and it showed she was hypo every night without fail and I used to get up every night at about 2 am and test and she was going hypo at other times. We had to come off Mixtard 30 immediately. We tried Novomix 30 and all the other combinations of Novomix and eventually Lantus became available so we were put onto MDI and have never looked back.
With MDI you have one long acting insulin morning or night which is Levemir or Lantus Glargine. That is the background insulin which doesn't have massive peaks and troughs, it has some little ones. The other insulin is purely novorapid (or similar) which is quick acting. You have to count the carbs eaten and then using a ratio worked out for you, you give the right amount of novorapid.
If your child is under 12 you can skip the MDI part. If he is that averse to injections (and I don't blame him one little bit) according to the NICE guidelines he can go straight onto an insulin pump which is an even better way to control blood sugar levels and you pretty much only have one injection every 2 or 3 days. The level of parent input is more with a pump but I haven't come across any parent yet who would not move the earth if they could for their child.
I'm sorry I couldn't give you the answers you perhaps wanted but I hope I have gently explained the better options for you. If you have any questions at all about anything ask and someone will be able to answer.
In the meantime take a look at
www.childrenwithdiabetesuk.org it is a website written by parents for parents like yourself. If you wish you can join the email group on the home page and you will then meet the other parents and children I was referring to above. A few are here but most are on that email group. You can ask the same question that you have here and see what answers come up for you.
Take care