Congratulation for that latest addition to your family.
I think that you are covered for a while with your lenses going up to 105mm. Of course, in 18 months or 2 years, you may find you need more reach to play outside, but right now, I'd refrain from buying a lens I don't need but that stretches my budget... I know, that is a bit of a dull advice, but you already have enough to take great images for some times. If anything, I'd buy a good flash and get used to using it for fill and bounce it.
I'd also advise you against the non L 70-300. That is the only lense purchase I made that I regretted. First, it is way to slow for anything inside and second, it is nowhere near sharp above 200mm. If was to do it again, I'd go for a 70-200 F4 as the 70-300 is really not providing anything useful above 200mm anyways.
Finally, if you do buy a non-IS 70-200 F2.8, i would not worry to much about IS unless you plan on using it for still life. In this range, most things I want a telephoto for require shutter speeds above 1/focal lenght (1/200s) anyways. You are not going to get a sharp picture of a kid at 1/30s as IS has no effect on the subject.
Mind however that I don't have first hand experience with the 70-200 2.8 (any of them) so I could only comment on their respective strengths and weaknesses based on reviews... and so I won't.
Have a nice time with your new kid (and kit).