Does it make sense, if someone invest $100k on me and I'd only require $90k, I take $10k and invest it back on some other people?
Your investors would frown on such a practice. They gave you money for X reason and you used it for Y reason. It doesn't matter what Y reason is or how noble the cause, it's still Y reason. Your investors reactions might range from nothing to outright anger to a lawsuit. Best case scenario, 1 in 1000 approves. Less best case scenario, they believe they own a piece of whatever you used the money on. Worst case: they withdraw funding and sue you for everything you spent. And more.
Things would be different after you start making returns on the investment, but by then you'd have spent that $10k on your own project for some reason.
In the end, keep the $10k, it'll be a nice buffer if you really only need $90k. Which I highly doubt. Did you budget in networking costs (that is, attending conventions and relevant social functions to gain new contacts and potential staff, plus gas, travel, and attire to said events)? Does it include the cost of treating your staff to an occasional morale-boosting event after a crunch time? Even if that's just pizza and beer, that can be up to $200 or more for a small group. Do that five times in a year, you've dropped a grand just on food. I doubt you've budgeted for things like that.
Don't cut yourself off at the knees just because you know people who could use the money.
No absolutely not! Don't do it. Your investors have invested in you and your business. The money is not yours, it belongs to your business and that is what it should be used for. If they wanted to invest in someone else, they would have done it directly.
When your business is running well and you are able to take some money out, go for it - with your own money.
This would be a highly undesirable behavior.
Your investors are providing money for you/your idea to build a company and get it off the ground. As part of this investment they have an ownership stake (presumably) in your corporation. Having that corporation then invest in yet another corporation will make the accounting rather cumbersome, to say the least.
Also, it's highly unlikely that you are going to know for sure this soon in advance exactly how much money you will need. Almost everyone ends up needing more money and/or has to cut some features and ideas from the initial product to fit the development into the allotted budget.
There is also the matter that many times investors take some kind of a participatory role in the high-level management of the companies they fund, or they mentor, guide, and consult with the founder(s) of those companies. It would be difficult for you to build your own company, plus manage all the moving pieces associated with investing in yet another.
So, while it is admirable that you would like to help another startup, you should concentrate on building your own empire first and save your VC desires for when you are ready to fully commit your time and resources properly.
Good luck with your business.