You need to make sure you are squeezing your core (especially your butt) super tight. Also, push up really high in your shoulders. That will stop you from falling over. Also, the way you kick into a handstand is different from a front handspring...when you do a front handspring, you kick your legs really hard to get over. A handstand is slow and controlled, so you don't have to push as hard to get up.
Maybe if you improved your shoulder and core strength you will have a stronger handstand which you can hold up for longer and wont be so wobbly. Over the Christmas holidays I worked on my shoulder strength and I can hold a handstand for a lot longer now.
Otherwise just do lots of handstands against the wall or with your feet being held by someone.
You do a front handspring or a front lumber-ish thing? My guess is the second. Don't let your tummy out. Think hallow hold while you kick up. Do some without making it to vertical on purpose so you get the feeling of not going over the top.