We all seem to be agreed here: if you want to fly and enjoy it, there is no point in fretting about progress at what is, after all, a fairly early stage in the training (which never stops, of course...).
My story might not ring bells throughout, but I hope parts of it might help.
I started to learn to fly in a glider and was HOPELESS, truly abysmally cack-handed. I didn't stop though, because I was probably too dim to think about it, but kept on, spending the pocket money, enjoying some occasional, temporary progress until I realised I didn't want to be anywhere else. The people I met obviously inhabited some superior world to my dull existence, but they seemed to want me to move there too. I still wasn't solo after %*$$$! launches but quite enjoyed having someone in the back to talk to and keep me safe....
One evening in the pub (which I couldn't afford either but that was part of the buddy system too) I learned from the guys that I was actually not far off solo, but seemingly lacked the motivation to be consistent. I didn't make much of an extra effort, because as has been said, you can't, but something changed and soon after I was sent off solo. From there, equally slowly, I progressed to other things. It all crept up insidiously and once addicted, I rebuilt my life around it. At one point when thing were particularly tough, domestically and it seemed I couldn't afford to keep my house, a change in the job yielded more money. Other problems arrived but somehow there was always a way to keep flying.
Of course your situation is unique and with family to consider you may feel guilty about the money spent on your 'hobby'. I'm sure you don't begrudge your family members their hobbies and they want you to be happy, so don't beat yourself up about holdays in the Bahamas. The point I'm trying to make, ineptly, is that even if you can't afford to fly as much as you want (who can?), if you are getting pleasure you will find a way. I'm not totally convinced by the 'you make your own luck' philosophy, nor that of Micawber, despite what I've written, but I do believe that if you can connect with the community prevalent in various areas of aviation, whether it's with microlights or gliders or the flight school at Elstree, any passion you feel will reap rewards. You don't have to have a specific goal, although much of what you read in the aviation comics might lead you to think otherwise. I certainly didn't ('I shall just keep on and if I make any progress, that's a bonus' was my mantra for a long time), but if you can look back on the last lesson, or any of them, with a degree of pleasure, there's your answer. Carry on while you can, for as long as you can. If you have to stop, you'll have logged experience that can always form the basis for a reprise in the future. Why think so negatively, though? You are flying now and although you've earmarked a finite amount, who knows what might change? Without knowing or wanting to know all your personal circumstances I suspect that there may be some wiggle room when you need it. Enjoy the journey and try not to worry so much. That's what makes it more enjoyable...
I'm sorry for the long post, much of which has just reiterated what others have said, more eloquently. I was moved to post again because I don't want you to give up on yourself. I wish I could say it better.