I think it's a little early to say your DD is being isolated. You should stay alert, but don't assume the worst. I think 95% of new moms who stay home with the infant are isolated. You're tired, probably worried about money, exhausted from lack of sleep and nursing, etc. Not a lot of opportunity to go out and about like you used to.
A lot of men are threatened/upset/bewildered by how much information women share - whether with their mom, sisters, friends. It might have been ok with SIL for his GF to discuss her finances with her parents or get their input on the car she wanted to buy or whatever. But it's no longer her finances or her car. It is theirs and he may not want his ILs having a say in their decisions. It may not be that he's doing a Jeckyll and Hyde transformation since the wedding. He may just be trying to establish firm boundaries.
I know the birth of a child can be a special time between mothers and daughters - it used to be that way exclusively since DHs were out hunting the mastadon or whatever - but in the past decades the focus has shifted to the specialness between the new mom and dad and baby. This may be another area that has your SIL uptight. He may sense how much you want to bond with your daughter and baby at this time, and feels he's getting pushed aside. And it doesn't matter how much actual time he is on sight versus you - it's the perception, not the reality that is important.
Of course, you could be 100% on target. Only time will tell.
Even with a baby doing the non-stop nursing thing (I had two of those), there are a lot of baby carriers that help you nurse in public with lots of privacy. I used a baby sling and often had people try to peek in to see the baby, not realizing what the baby was doing. With a little practice, she can take the baby out and nurse and not be embarrassed. It seems intimidating at first, but like another poster pointed out, it only gets easier if you practice.
You say your DD has lots of friends. Have they talked to her or come over? If so, I would be less inclined to view your SIL as trying to isolate your DD. If they haven't, try to find out why and maybe suggest your DD get some girl time with her friends.