Having worked as a drivers mate and also driving a 7.5T along with being a Forklift Operator and an MHE Instructor I personally would stick with looking at FLT Operative, especially given the "new" family aspect.
The difficulty with both is initially getting work because you can get stuck in the catch 22 of "no experience - no job" and unless you are working for a company who put you through the training course it can be difficult to get the experience.
Salaries will vary depending on where you live and the hours/shifts you work. I have seen FLT drivers being offered £8.50 an hour up to £15 an hour but it comes down to the equipment you can operate and your experience again.
Remember also that with FLT work you may not always be on the lift truck as the majority of employers tag on "other duties as required". The advantage is that you do normally get to go home at the end of your day which is not always the case with LGV drivers.
If you want to be there to see your family then FLT is the better option and probably offers more scope for progression given the number of different trucks you can learn to operate.
If you are going to go down the FLT route, I would suggest getting at least Reach and Counterbalance initially and check all the available job sites for listings in your area to see what truck types are being listed as required.
Finally...good luck.