You're both so impressive - at 19, to be working, studying, owning your own home, planning for the future - I was a CHILD at 19.
The problem is, the in laws see you as children. You're where they can keep an eye on you, because children don't get privacy or have the right to their own space. If you were to have a baby, that would be a third child under their control.
No point going over what they said or what you thought would happen before you moved in. Can't change that.
What you can change is how you manage the current situation.
I think you've already changed the locks?
I'd also add a camera for general security but also to see if they do come in while you're out. If there is no evidence, that would reassure you.
Communications. You and your DH need to present an absolutely united front to them so it does not seem to come just from you.
Email them to explain that now you're both in a new stage of life as independent adults you both require a different approach. Talk about boundaries, privacy, consideration for space etc. Explain you'd love to see them when you're expecting them and ready for visitors. State your policy about spare keys. Always 'we' not 'I'. Sign it from both of you.
Assertiveness is hard but can be learned.
The three part sentence 'We understand ... however ... therefore ...' is a great help:
'We understand you like to feel close to us, however we do need privacy and space in our new life together, therefore we need you to call or text to check if we're ready for visitors before coming over'.
Broken record:
'As we say ... ' Repeat. And repeat .
Tone of voice in writing and in person - polite, pleasant, neutral and reasonable language at all times, no matter how you feel.
They're having to learn new behaviour, which takes time, and can be tiring and exasperating for all, but they can be trained.
And praise and thanks when they get it right.