The problem with giving ultimatums when two people's happiness is in the balance is that the party who "caves" to the ultimatum of the other will forever be resentful. If his own happiness and mental health are affected by a job then he may see this new offer as a solution to pull himself out of depression and unhappiness. Do you want to be the person that denies him that?
So, rather than tell him he cannot take the offer, you must present the problem you describe of "less income to pay for a housecleaner." But be warned, you will have a more successful conversation if you are very careful about your choice of words and try to isolate the problem from the cause (i.e. new job).
So, how you go about this is tell him that you support any decision he wants to make about his job but want to talk through the financial, logistical and schedule changes that may be affected.
Then, ask him to take the first stab at what could be affected. If he is the one to identify and voice the concern first then he cannot blame you for being negative about the offer.
Once the issues are identified and documented . . . (have a notepad out for this conversation), then you move to the solution-izing part of the conversation. And, if he fails to identify the issues, then that is where you do.
With solution-izing, again, give him the opportunity to take the first stab at things, but do come to the conversation with ideas. Do NOT place the burden all on him.
And to do so, you must reconsider your "black and white" viewpoint at the issue and solution. Right now, you assume (and it is a strong assumption nonetheless) that a reduction in his pay and two nights away will not allow you to have a cleaner and will place an extra burden on you.)
However, are there other household or personal expenses that can be reduced or eliminated that may allow you to keep the cleaner? For example, if you have several streaming services that are not a necessity, and perhaps, even more "his thing," maybe getting rid of these is a consideration. Perhaps, you both could make an adjustment, or maybe he needs to adjust his expenses more so since he will bringing less to the nest and will be away more frequently.
But this only addresses one half of the deficiency in your home life created by his job change. The other part is what happens because of his absence. Undoubtedly, taking on the sole child-rearing duties and transporting children here and there by yourself 3 nights a week will take its toll on you physically, emotionally, and mentally, if you are NOT given opportunities to rejuvenate mind, spirit and body.
So, part of this negotiation must be a frank discussion on this topic. He must be made to understand that he must take more of the childrearing tasks on when he is home to give you a break.