What do you want long term?
Do you have kids? I'm guessing not. I think as part of thinking through what you do want longer term, put that into the mix.
Personally, I don't think an 'arms length' relationship is likely to work for you long term really and that goes triple when you have kids. I would be super wary of having a routine established where your partner goes to them to continue their relationship with you not there. Pretty soon MIL might come to realise she quite likes that - she can't come into your home and control things, but she can quite easily reframe the situation to see you as having been 'got rid of' and no longer welcome in her home - but her boy can come back to mummy and be fussed over. And with you not there to hear, if your DP likes to keep the peace - he might think he's done pretty well at following your wishes at keeping her away and so will be more willing to turn a blind ear to sarky comments about you (what you don't know won't hurt you) and might think that telling his mum this and that about your life in order to make her think she's got more input is worth it if it shuts her up. Things you'd rather not share... but you're not there to hear him mollify her.
It's ultimately very divisive and corrosive for your marriage. Here's an example. You're redoing the bathroom. MIL is full of it on your DP's visits with advice on what tiles to use and where to go and she knows best of course. Your DP treads a careful line with 'Yeah thanks Mum we'll bear it in mind'. FIL is pulled in, before you know it peacekeeper DP is accepting their advice on tiles in order to stop the tide of interference, you aren't there so least said soonest mended - you end up with tiles MIL has effectively recommended but you have no idea of this until a year later when she sees the bathroom and smugly comments on 'Oh I knew the tiles I chose would look perfect.' Trivial and so not trivial.
You won't know what she's saying to him and if he's a peacekeeper he won't tell you it all.
That's before kids. No aspect of this arrangement will work for a second if you have children - you absolutely will not want them to see her without you there. And you shouldn't, because the subtle undermining and 'Oh we don't have to listen to silly Mummy's rules when you're at Grannys! That's why silly Mummy doesn't come here, we have fun here and she doesn't like fun does she? Shh don't tell Daddy now' - that kind of shit very soon hits that particular fan and well, it ain't good for anyone.
So. What to do. Are you prepared to talk through with your DH about what happens if you have children, and how he'd feel about her not seeing them? That effectively if you're going to be a proper partnership, there cannot be a dynamic where he continues to be part of a family that you are NOT part of?
None of this can work long term. The two answers are that you see MIL and FIL together as a team on controlled visits, that FIL is still welcome to yours to see your DP separately, and that you maintain the same when kids arrive. The other answer is that he cuts contact. The third answer is that you move far enough away so that contact is controlled via the distance.