What a heart-wrenching post, and I am very sorry to read of their passing, especially so soon one after the other.
They sound like very special piggies, and people should never underestimate how important our furry companions can be to us in our lives. The grief can and often is just as real and genuine as any other type of grief.
I cannot tell you what to do, how to deal with it, or how long it will take for you this wretched feeling to fade, but there will come a time when thinking of Leyla and Roxi will bring a smile (even though tinged with whistful sadness) instead of the raw grief that you feel right now.
For me the best thing that I could do in this type of circumstance would be to grit my teeth and go and see the baby piggies, and watch them a while. I would do my best not to compare them in nature to those departed (hard I know, special as they were), but to allow myself to notice their own little quirks and ways, and give some little treats to them, as it feels good to give, even when you're deeply sad. Allow them to give comfort in them just being them, and have faith that a bond will form. It will never be the same bond, as no two are the same, but a bond none-the-less.
I (in this circumstance) would also do my best to see to their physical needs, on the occasions where I am stressed or upset and my initial reaction is to put it off, I always feel better having cleaned them out and refreshed their food and hay.
However we are all different, and I can only say what I would do. It is good that you have the support of your partner and sometimes having a break and allowing time to grieve and think of your own needs only for a while can also work, but I would advise not to do so for too long, as grief can take over your life otherwise.
My First hamster was special. Really special, and when she died my next just wasn't the same, and I couldn't warm up to her quite the way I had with my first. The grief I felt for that hamster had been very real, and this new one just didn't fill that gap because it was a gap that couldn't be filled. I did however spend plenty of time with the new hamster, and we did bond, and I grew to love her more each day, and appreciate her for herself. Likewise my first Piggy was special to me, having come from a bad home, and having watched her slowly gain confidence and trust, and live the life she should have been living from the start, she became especially dear to my heart. I also miss my others - Cloud, who wouldn't be touched but loved to sit on my slippers and jump onto my lap, and Snowball, who was intelligent and people-friendly, and enjoyed snuggles. It can take a while to come to terms with their passing.
When I was younger I had a dog. He was my one true companion through me being badly bullied through school. He loved me, and me him, and it's the pure love that you get from animals, never playing tricks with your emotions, or scheming, or caring what you look like, just pure love and trust that goes both ways. I found it tough when he passed away too. I just had to get on with other things, and redirected my love and desire to nurture onto my rodent pets. It's not a case of pulling yourself together, as that's not something you can just do, but to focus on caring for another can help to take away the focus on your own grief, and give a sense of purpose, which is why I recommend, if you can, spending some time with your babies as soon as you are able to do so, even though their care is currently being done..
Lots of hugs x