Focussing in live view is really only useful if you are shooting things that aren’t moving and generally only on a tripod. It is great for macro or product work but less so for portraits.
What I mean with front focus can probably best be explained with this shot http://jessicarachelo.smugmug.com/Kids-and-Babies/i-4pHJXdJ/A . Camera AF will, if you let it, select the closest point within the AF pattern (within reason) that has the highest contrast. Her black and white jumper is a perfect AF target and this is why her sleeve is sharp but the kids eyes are soft. This shot in particular is suffering a bit with perspective. It looks as if you’ve used a fairly wide angle lens to fit the three of them in which has distorted the perspective somewhat and made her arm big and their noses bigger than expected. Looking at it again (on a colour calibrated wide gamut monitor) it has a quite obvious green colour cast. Last time I checked it was on my cheap TN screen where it wasn’t very obvious. The skin tones aren’t great and uneven. Are you using a grey card during your shoots? Have you got a proper screen that is colour calibrated? If you don’t have these things that would be a strong suggestion of mine to get and that pretty quickly. Nothing good is going to come out of having wonky colours. In fact your self portrait has some of the same problems as the shot I linked (short focal length and green colour cast)
As for the focussing, it is vital not to let the camera do the selection apart from in some settings like fast paced sports with long teles or kids in some circumstances. As for one shot vs servo, have a look in the camera manual and it’ll explain it far better than I can but basically one shot is for static subjects and servo is for things that are moving. Toddlers often benefit from servo focussing given their tendency to run about. What camera are you using? Some will have a lot more tweaking of the AF system possible than others.
Your website makes a lot more sense now and is easier to navigate. It looks clean and modern and works really well with the beach theme. The shot of the dad carrying his kid towards the water is lovely and sets a nice tone. I would probably get rid of the little specks which I’m guessing are birds as I started scratching on my screen thinking I had bits of dirt stuck on it.
I would also suggest making yourself familiar with printing the photos as you will need that if you want to take it further than short sessions for a hundred bucks. It will also give you a far better source of revenue if you have decently priced prints available made at a proper pro lab. I would suggest printing yourself a portfolio in good size, either 8×10 or 11×14 because this will also be a great selling point if you have a coherent paper portfolio. For printing a colour calibrated monitor is essential. Before you get them printed I’d suggest re-editing the lot with all you’ve learnt since you started and make sure they are consistent in both colour and contrast. When you put them back on your website it will look more consistent and professional.
Good luck and make sure you pay your taxes and insurance!