I think op your having a hard time here because a lot of people seem to be commenting from mums perspective and aren't in a blended family.
I'm a mum and I totally wouldn't want to go into my ex's house, but then I'm not the type to push boundaries and think because my ex had a child with me that it gives me license to wander around he house 😵💫 are people really thinking this is ok with teens ? 😵💫 maybe small children it's slightly understandable.
But you aren't dealing with this type of mum. So that changes things.
A key safe with the key removed when they aren't there would be my vote and a ring door bell. If they let mum in just once, or mum comes by on her own to "drop" something over, then it's removed and you show them why. So they understand why.
Teens are going to push boundaries- if they have a house party then they lose the key and that's done.
Your totally within your right to say no you don't want mum in your home, and I'm glad your ex is in agreement. Just because your married to someone who has a child/teen, doesn't mean you have to allow people into your space you don't want to (aka mum, parties ect)
We had a problem with DSC doing this I came back to find mum reading out post having a cup of tea in our kitchen. Scared the lights out of me. DSC said she felt she couldn't say no to mum. Mum is lovely but lacks normal boundaries- I did say ok next time I will come have a cup of tea at your when she was at work and she looked horrified... saying it was different.
Which of course it wasn't.
Tbh I was more worried about house parties with a teen I remember (just about when I was that age) so prompted a change in things.