Suppose there is a recession, and the government aims to provide a fiscal stimulus. Assuming an independent CB, the government will issue treasury bills to borrow and finance the stimulus. Consider the simple case where all treasury bills have zero coupon, and have a face value of 100 to be received in a year. The market for such a bond would have a price. For example, the bond can be purchased for 95, and will give 100 in a year making the interest rate 5.2%. If these bonds flood the market, this price will go down. Consequently, the interest rate will increase.
At the same time, the CB which is independent, wants to boost the economy through a monetary stimulus. This is because this recession is one with very low rates of inflation. It does this by lowering the rates of borrowing so that people can borrow and purchase more.
How do we know that which of the effects will dominate? Are the monetary and fiscal policy working opposite to each other? What am I getting wrong?