Op, I dont think you are being unreasonable at all. If half the money is your dads, he can do what he wants with his half, as long as there is plenty to cover bills and general living costs. What exactly does your mum object to?
DH and I are in a similar position to your parents, have built up substantial savings/shares in individual ISAs, but then have a joint account that salaries go into and a joint instant access savings account.
We have 2 young adults, one working on a year out from uni, the other on a gap year with a retail job. We pay money into a pension for them and also give them additional cash every now and then eg we paid petrol for both of them to join us on recent holiday. I just transferred the money to them, didn't discuss or agree it with DH, he wasn't bothered but even if he had been, I would just have said that it came from my half of the account! DS said it wasn't necessary, to which I replied, I know, but I want to do it.
I have both their bank account details as we regularly repay money to them eg if they buy shopping for us, esp DD who works in a large supermarket.
They both have an inheritence which is feeding into an ISA for houses eventually, but I can see us giving them lump sums in their twenties, or maybe taking over the ISA drip feed for a year, simply to pass on our wealth now rather than when dead. I dont think DH will disagree, but again, if he does, it will happen anyway, out of my half of the savings.
Whats the point hoarding the money, just for them to then pay inheritance tax if we died. We have reached a point that if we both died tomorrow, then our savings and house will exceed IHT limits, we are not massive spenders on a day to day basis, so we may as well help them as much as we can, without spoiling them. Yes, some of what we have is intended to help retire by 60, ahead of pensions kicking in, but I cant see us ever spending everything we have, unless/until we go into a care home eventually.