That's also in the best interest of that investor. Structuring and managing relationships is one of the things a CEO should be good at if the company is to become successful. This goes for the relationships with the rest of the company management, it goes for outsiders and it goes for the board.
If a CEO is hired by the board then that changes but if you found it you should be in charge and you should make it clear - in a respectful way and if necessary by educating your board members - why that is the case.
> If you depend on that outside investor to support (take pro-rata, say upbeat things etc) your next round
He or she will say upbeat things regardless (because they're already in it is in their own interest), whether or not they will take pro-rata shares with a next emission will depend on the price and their ability to purchase as much as anything else so I would not count on it regardless and take it as a nice-to-have but not a must.
If you behave like someone else is in control they are in control. Don't do that.
Even a hired CEO has a mandate and the board can fire him/her but they can't unduly influence that person beyond supplying (possibly unsolicited) advice. Otherwise no CEO would ever be able to do their job. Ultimately, whatever happens is the responsibility of the CEO and the board is a source of advise and makes sure the CEO does a good job. If the board is backed by the shareholders they can fire the CEO, but if the shareholders (and in this case that meant the original founders) don't agree by simple majority to get rid of a CEO then he/she can continue to do their job. Whether you still want to is another issue entirely.
Anybody in a CEO position would do well to make sure they understand their rights, obligations and their relationships with the various other entities they are dealing with. If you don't understand those then it is a recipe for frustration and potentially disaster.
This is the reason why you'll see board members leak to the press (see for instance Yahoo! recently). They can't win the argument in the boardroom and they can't/won't fire the CEO (maybe because they only have a minority share and the rest of the board and/or shareholders do not see their way).
This is also why founder disputes are extremely risky for a company. Founders typically hold large blocks of shares and if some those suddenly align with of non-founders then it can really break your stride or cause serious trouble.
Say a company has two founder that still hold 60% of the shares, 5% is in an option pool and 35% is held by an outside investor. If the founders no longer see eye-to-eye the board suddenly holds the tie breaking vote and this could lead to the departure of either one of the founders depending on with who the board sides. In such a case I hope your shares are vested if you're the founder that is forced to leave (and if not I hope you have a vesting acceleration clause in your contract).
Y combinator is a real game changer in many ways, and one of those ways is that founders now find themselves with a support group of others who have been in similar situations and who have a lot of knowledge about subjects like these. But there is a large group of founders currently not in YC and for those especially it might be advantageous. As a small time investor I'm sometimes in the role of the procedural jerk who makes sure that from the founders perspective all the i's are dotted and the t's are crossed. Usually this is not without friction but I've yet to hear a founder not express (sometimes many years later) that they're happy we went that route. Experience - even a little bit - can be worth gold if there is a power asymmetry and such asymmetries are more the rule than the exception where founders meet capital.
That's a relationship that you will have to manage, that's for sure but if you see him as your boss you imply that he has the right to throw you out or sanction you and that isn't the case, as majority share holders you and your co-founder should be in control of the company and the board should have an advisory role. If the company goes public, hires an outsider CEO who is not a part of the founding team or if the founder-CEO is not seeing eye-to-eye with the other founders then the board can become more dominant.