It's nice to see a post on this subject as our family are also planning to re locate to Malta in the next few months. We do have a few family and friends on the island but it’s a lot different to actually move lock stock and barrel compared to a holiday.
I’ve got 2 children aged 11 and nearly 3 and it’s a wonderful place to bring up kids in my opinion as I’ve been there many times over the years and always felt safe. When we relocate I will look after my kids full time as opposed to now where they are with carers whilst my husband and I both work so I’ll also be keen to find entertainment for my 3 year old.
From what I can see you will have no problem finding rental accommodation as there seems to be plenty available which look clean and attractive and I’m sure there are loads of playgroups and nurseries as the Maltese are very family orientated. Also, an added bonus is that everyone speaks English (but I am currently learning Maltese via cd rom).
As for the weather, well, I’m pretty sure it’s going to be better than the UK anyway.
I also have a few concerns similar to yours but I’m sure it will be fine as I’ve been there with small children/babies and never found day to day life a problem. I once badly hurt my back whilst there and needed a Doctor quickly. My inlaws GP came out within a few hours and was kind and helpful.
Good luck and it’d be great to keep in touch and compare notes.