"Attempts to prove one's value are altogether futile. No proof can bring lasting self-confidence to anyone who doubts himself; no circumstance can be too trivial to serve as a testing ground for the uncertain." - Rudolf Dreikurs
This goes for parents as well. It is always a mistake to try to prove to your children that you love them. All you need do is ask yourself, "Do I love my children?" If the answer comes back "yes," then you are free to go about the business of being a parent to your children. All attempts to prove to your children that you love them will lead to disaster. Your children will quickly learn to exploit your insecurity by demanding evidence that you love them. These demands will gradually become more and more outrageous.