BEFORE, you drop and change your auto insurance, you need to find how much of a discount you get for the multi policy discount. My "guess" is at a minimum of 10% to 15/20%.
Years ago, we had our homeowners and my (late) husbands auto on the same company. When I got a quote to add my auto (3rd) policy, my auto went from $900 to $500 a year, or a savings of $400.
Normally, your mortgage payment is based on the loan amount, property taxes and your homeowners insurance that is divided by 12 months a year. Now depending on how much more you lose from the multi discount, they "might" adjust your monthly payment to total the new amount of the higher homeowners insurance, or adjust at the end of the year. I "think" with ours, our lender would send us an adjustment every 6 months if our payment went up or down, which usually in most cases if higher was our property taxes, but since my house is paid off, am going by "memory".
If you are lucky and have an agent, they can tell you how much the discount and with the new policy, would it be much less and best to change or (not).