This was me 2.5 years ago.
I had a just turned two year old and was pregnant again with her brother. I had bleeds, nausea and low mood until 16 weeks. Then I was reasonably good all the way through.
What I remember looking back on both my pregnancies was between 6-12 weeks with both I felt low and poorly constantly. I guess the sudden surge of hormoneswere to blame. I hated the first trimester.
Like you I had the guilt. I was a boring mum for a couple of months. I couldn't be arsed to meet friends or go out. When I did go out I had crisps in my pocket to settle my sickly stomach. I remember going downstairs with a bucket in the night feeling sick as anything and sitting on the sofa.
I remember around 7 weeks with my son just sitting on the decking outside. It was a hot day and my DD was playing happily in the garden. I just thought I don't know how the hell I am going to push through this next 6 weeks.
The thing is you just do. You keep going. Every day is a day closer to that first scan. Once you get to ten weeks you are in double figures and very close to the next stage.
My advise is do what you have to do.
Playdoh, megablocks, Duplo, colouring, extra Tele and biscuits too 
order some cheap stickers from eBay and let them play. Magnet numbers or letters to play on the fridge with. Sit them in a highchair with water and dry pasta etc. Literally anything to occupy them so you can just rest.
It's ok not to get dressed. It's ok to lay in bed and let the little one watch tele on a device for half abit.
If the weather is dry. Open the patio doors or whatever. Sit outside on a chair and breathe in the fresh air. let your child run about and play outside. I promise you they will never remember this as being a boring time. They will be perfectly happy.
Mine are now 5 and 2. I don't regret it. I love our family. They have a great bond. As people they are opposites. They have been opposites in everything from sleeping, eating, playing, affection, fear and confidence. Your experience won't be the same second time around. But you will do it because you are the mum and we just do it. We adapt and get into a new routine. The first couple of weeks were chaotic. Too many people coming around and I felt overwhelmed trying to keep the house in visiting condition and get sufficient rest on top of two kids needing me. But then once all that was over (2.5 weeks in) we got into our own little Rytham. Babies sleep quite alot in the day so there's plenty of time to bond with the toddler. By the time the baby is that bit older you don't remember your life before and you will just do it.
Congratulations and don't worry. Do what you need to do and you will all survive. You don't need to be super mum right now. You just need to be mum xx