Maybe I missed it, but why are you offering her 3 weekends a month. Equal weekend time is fair and just.
You are already shouldering the heavy load of the parenting, you should be able to have equal "fun" time. Your kids need to be able to see that you have down time or it can set them up to assume that the inequality of having one parent be the "stable solid parent" and one parent be the "fun parent" is a normal thing. I know you enjoy any and all time you have with your kidlets, however that time is filled with obligations and homework and weekday responsibilities. It is unfair to you and them that you don't get half of their "off" time. I get that her schedule gives her a reason to not be active during the week with them (and a lot of times I think that's part of the lure of the jobs WS's take - just be home when there aren't as many tough jobs), but that shouldn't preclude you from having some down time with them.