It might be irrational and unreasonable OP but it's entirely understandable. I don't think you sound unhinged at all, just stressed out and grieving and sad.
Secondary infertility is shit. I've been through it, had two miscarriages and years of trying and failing to conceive and I experienced very similar emotions to those you have described. At one point I was the only mum at preschool who had neither bump, baby, younger toddler or older child at school and I hated it. Hated it when random mums I knew a bit fell pregnant, hated that I had to really try to be happy for friends who fell pregnant, and hated it even more when they tried so hard to be sensitive about the fact that they were pregnant and I wasn't. Cried for hours and hours when my SIL fell pregnant with DC2 at the height of it all. What you are feeling is normal.
(FWIW, Kirstie Allsopp was my 'hate' outlet when I was trying. I think she's ace, normally, but can vividly remember reading a quote from her blabbering on about her second pregnancy "So there'll be just two years between them, which is great because it is exactly the age gap we wanted!"
God I hated her. Hated, hated, hated her. And hated the actress Hermione Norris too because she'd her first child a month before I had mine, and delivered an effortless second the month I should have been delivering mine, except I'd miscarried, and she hadn't).
Grief and pain are irrational. Toddler groups, parks, softplay, birthday parties et al are a living hell when you are trying and failing to conceive DC2. FWIW, I found the easiest answer to anyone asking 'about number 2' is to be brutally honest. I used to take a perverse pleasure in making people squirm, there was a part of me that wanted them to feel guilty as fuck.
(See? I am just as unreasonable and bonkers as you think you're being, and that's even having - eventually, via assisted conception - managed to produce a DC2). Just reading this thread stirs up all those emotions all over again.
The only advice I will give is to be gentle with yourself. Accept that these feelings are normal and understandable, and try and deal with them as best you can. I used to allow myself what I'd call 'bad baby days' where I would just acknowledge that I felt like shit and make sure to do something nice (cake in a coffee shop with DC1, a glass of wine for me in the evening, a new bit of makeup or a new scarf or something) for myself, just to try to take the edge of the shiteness.
Sending you an unmumsnetty hug.