Hi OP,
I have a massive amount of sympathy for you. It's the toughest time when the second child is still preschool. I remember thinking it would never end. People said: 'only a couple more years of this' and I wanted to howl because two more days felt too much, let alone two more years. We had no help from family either and it was so challenging for a while.
Here's stuff that helped us through a very similar stage:
Break the weekend into four hour chunks - four each day plus 8 hours sleep (hah!) Eight chunks of time in total.
Have one chunk each as adults on your own. You each get a four hour period at soem pre-agreed point during the weekend to do whatever you want wherever you want. If you want to lie in, then have a bath, it's DH's turn to do all childminding, and that includes removing a child screaming 'I want mummy' from your earshot. If he knows he gets four hours too, then he will be OK with it. Go out shopping alone, or for coffee with mates or to the gym or snooze in the sun in the park - totally claim those four hours as your own, and be very supportive of DH doing the same. It made a massive difference to us.
Then, each day of the weekend, have four hours family time. Make a big effort for it to be calm and fun. If DD is still toddler-bonkers and lively, take this into account. Go to play farms or swimming. Do something that helps her run off energy. But practise having fun as a family. That was a bit shift for me. I stopped being desperate for the kind of fun I used to have and started focusing on fun for all four of us. You end up feeling closer to DP when you've had a good family day out. They take practise. If DC pick up on the fact that you are looking forward to spending time with them, in a relaxed mood, it helps. Don't have high expectations, just muck about together. If you're all knackered, just carry a picnic into the garden and turn the sprinkler on etc.
The other chunks of time are for routines - eating, cooking, bedtime etc and for chores - shopping, cleaning etc. Helps if each adult takes one child along for this stuff. The DC get some one-to-one time with a parent and are usually better behaved than if they're together, and you can focus on teaching them a bit how to sort laundry or fill a shopping trolley.
It's not much, but that four hours a week alone plus four hours each weekend having fun really altered how we lived.
And while you're both so knackered, cheap tricks like frequently referring to why you fell for him, or reminding each other of lovely moments throughout your marriage helps you remember this is short term, not a sign you aren't compatible. It's OK to be knackered for a while. It's OK for the highlight of your week to be a box set you watch together over a glass of wine with a child coming back down stairs every few seconds.
We managed very few dates at that time, but we did learn not to make them dinners out. Sitting over dinner, trying to vow not to talk about DC when you are stoned with exhaustion makes you feel your marriage is over. Go to a comedy club, to a stupid action movie, to a gig - something where you don't have to make any effort except being entertained. Live music and comedy gigs worked best for us as they put us in good moods.
I promise this all gets easier once DD is in nursery.