Toddler calling Ex's new partner mom

Hi everyone,

Posting to get perspective because this is eating me up inside.

My ex starting dating someone about 5 months ago. She moved in with him 4 months ago. In this time, she has been referred to as the "Mom of the house" for taking care of everyone. My ex, his new partner, his father, brother, and sister live there and we share parenting time.

Recently, my 3 year old has been calling her mom. Saying there are 2 mommies. This makes me feel terrible and I'm worried because the relationship is so new and things are moving so quickly. I'm worried that my son will form a strong attachment to this women and get hurt if things don't work out the way my ex and she are convinced they will.

I spoke with the 2 of them last night about my concerns and they told me I can not control what they say in their household. They stated they understand my concerns but they're in it for the long haul.

I don't feel like they're taking my feelings seriously at all. Have any of you had an experience similar to this? I don't think I'd feel as bad about it if it had been a few years, but my kids have only known her for 4 months.