I don't know much about Lucille Ball autographs at all, but, in general, I would strongly recommend avoiding both of those dealers.
If I was flying blind and had to pick from the three posted, I'd say the PSA/DNA cut you just posted would be the safest bet.
There are some for sale on R&R Auction, but they wouldn't be items you could get in time for Mother's Day:
Here's another from Rolf Ramsier. Again, I'm posting these based on the good reputation of (and my own confidence in) the seller, not my own knowledge of Lucy's signature.
I'd wait for more opinions if you can. I personally don't like recommending solely on the basis of JSA or PSA authentication. Both companies have their share of issues. I'm surprised we haven't had any more input thus far. Given her level stardom and legacy, I would think that some people on this forum would know more about her signature.
Depending on how much you want to spend there are Lucille Ball checks out there. You could have that matted and framed with a "still." That would be the safest way to have an authentic autograph. That or there are Lucy and Desi signed contracts also. You would have to factor in matting and framing though.This is an example of a signed contract
Wow that is really great. You are a good son I am sure your mother will be very happy.