eh, some babies are just intense and want mama. Sometimes, that sucks for mama. My daughter wouldn't even let my husband hold her for more than a couple minutes without screaming for me for the first 6 months. I had no inclination to force that on her, or on anyone else. I kept looking for glimmers of her being ready, following her lead, giving gentle nudges, but never forcing her to be with someone when she didn't want to. She was VERY attached to me through her first year and had intense separation anxiety. It's just her personality, the way she was built. The first time I was able to comfortably and regularly leave her for a couple hours was when she was about 18 months old. Yeah, that was a real drag sometimes...but it was only 18 months out of an *entire lifetime* - pretty short timespan in the grand scheme of things. And I feel like by respecting her real need for me in the early months of her life, she was secure enough to separate from me as soon as *she* was able/ready. She is now almost 3-1/2, and is not clingy. I'm sure that family and friends thought I was crazy and coddling her, but I saw zero value in forcing her as a preverbal toddler to be unhappy just to "get used" to other people caring for her. (Obviously, if we had to be separated for some reason she would have been forced to get used to someone else, but I wasn't going to make her 'practice' for that since there was no regular reason fro us to be separated).
I say honor the baby, and don't let anyone convince you that an infant "needs" to be used to other people or "has" to learn to have others watch them. If *you* want to get some time to yourself, that's one thing and just slowly try to get time away for small increments of time, and increase little by little...but I wouldn't let anyone strongarm you into thinking that because she cries for you at 4 months that there will never be another opportunity for you to help her become independent - there wil be hundreds of opportunities to help ease her into independence, doing it when she's not even been earthside for half a year seems so ridiculous to me. Can you have a date night with your hubby while she's asleep? Light candles, make a fancy dinner or rent a romantic movie, take a bath together or something like that at home?
Oh, and for whatever it's worth: my firstborn was not like this at ALL, he woudl go to anyone and be happy without me for hours...and I parented them both the same way - it's all about temperament, IMO.