Two is classic separation anxiety time.
I am a fairly laid back parent, I'm extroverted and I don't do routine and from five months my daughter has spent whole days away from me while I was at work (with her Dad or her Nana). And at almost two she was exactly as you describe - she's only 2.3 now, and I took her to a petting zoo yesterday, and she was terrified, like crawl-up-my-body terrified, of the baby chicks and the little bunnies.
It's just a phase!
The fact that you've had another child will probably be making her feel more insecure as well, and she's clingy because she wants to know that she's still your little girl and your special baby.
your DH, on the other hand - where the hell does he get off making you feel so ashamed that you name change on a parenting forum because he's told you that you've ruined your not-even-two-year-old daughter? When you're dealing with an eight week old as well! Jesus, what a total utter twat. Who the fuck died and made him the King of Parenting?
Seriously, OP. Do you, or he, spend more time with your children? Do you, or he, respond at night? Do you, or he, soothe their crying and learn their wants? Do you, or he, understand your daughter's emerging language better?
You, right?
So why the hell do you both think he knows more about parenting your daughter?