Celebrating a birthday is not a disfellowshipping offence. It is definitely not a common practice among members, but your wife will not get kicked out for it even if she wanted to celebrate with you and your child.
*if she was a pioneer she could lose priveleges though, due to not being 'exemplary'.
Plus reasoning that there is little difference between an anniversary (which most witnesses celebrate) and a birthday (anniversary of your birth) she might loosen up a bit.
The whole forbidding of birthday thing has no support scripturally or even logically in the context of witnesses observing wedding anniversaries. They know this, that is why you can still celebrate your birthday and be a Witness.
Path
(edited for spelling)