Op, there seems to be 2 problems.
Finances. Its all one big pot really. With him being a lower earner, you may find he does get a big portion. So tread carefully and take time to understand your position an decisions. But its joint assets, including your pension and the house. I am guessing his father's house isn't worth enough to negotiate him keeping that and you keeping your house AND all of your pension.
As for time for yourself. You are stressed so you are there every day when she gets in. At 13 she could let herself in. Even if it's just some days. Sounds like you need to slow down. She isn't a baby.
My oldest doesn't go to her dad's. The youngest rarely goes now. I know what ots like. But right now, you need to work with what you have. Pushing dd to go spend nights at his so you have alone time isn't really going work and will make her feel worse. Its a stressful time for all of you. A teenager will struggle if they feel both parents don't really care. And I know you do care. But their perception can be different.
If you really can't leave her for a day or she doesn't have friends she could spend the day with. You may need to accept you can't have days out and evenings away until she has got used to being alone, sometimes.
Its not really fair. But it's how it's worked out. I learned its best to ignore what's fair and what's not and just deal with the situation as is.
You really should be able to go out for a meal now she is 13. So start building her up to be left. Try and set some boundaries about you having alone time. Even if it's starts with 'I am having a bath. You need to entertain yourself'.
As a single parent, especially, when first finding your footing you have to grab half an hour or an hour where you can. Rather than when you want.
But soon she will be ok more on her own, want to spend more time with friends or doing her own thing and your time alone will come. My kids are similar ages and ots so much easier, now, than it was 5 years ago. It will get easier