Hi OP,
I think I have a slightly different take on this than previous posters. Rather than worrying about pensions and investments too much my first priority would be what can I do to plan for my kids needs and get us a holiday (each year if possible) having not been on holiday in 5 years. If they are teens in another 5 years they will be young adults maybe have left home.
You should of course continue to pay into your pension as standard (through work?) and continue to pay off the buy to let. If the BTL gives you 8k a year after costs (before tax) that is 8k to add to your state pensions and your private pension when you should be mortgage free and less/no kids costs.
The buy to let mortgage has 20 years to run. Is it interest only? The most I would aim for (if it is realistic) is to work out payments to pay it off over the 20 years (you would be 60). If that's not realistic pay a fixed affordable amount each month and refinance at 60 when the mortgage expires.
Don't overpay your own mortgage. It finishes when you are 56 anyway. You can't afford to.
The kids
Do they get pocket money? My son is 12 and gets £30 a month into his bank account. He can choose how to spend it to a great extent but he does go through us so we would try to dissuade spending too much on online coins for example. When he asks us e.g. for £8 app I would say it would come from your money he often changes his mind! He would eat Dominoes/subway every day we tell him we will get him one a week. More than that he has to pay himself but remind him of the effect of that on his money. At birthday/xmas if he wants a large ticket item we put £100/£200 towards and he has to save the rest. We have also told family when he is saving for a guitar/computer could he please have money towards it rather than gift. Make sure the teens know money is finite.
Encourage the teens to get jobs at 15/16 to top up their spends and hopefully save some. Have an amount you will pay for trainers/jeans etc and more than that they have to top up.
How much is in the trust funds? If it is more than 2k I would stop adding to it. They gain control of it at 18 and could spend the lot on a summer in Ibiza!
Driving lessons/car/insurance
I would put 2k of the money aside for each child (you have 2 I think) towards these. Be open with the kids that they have 2k each for this. If it pays for their lessons then they will need to save for their own car. If they work and pay for their own lessons it will be there for a car. Realistically they will probably need to pay their insurance monthly if they are working or wait to get a car until they are.
Uni. Depending on your household income you will be expected to top up your kids income if they go to uni. You need to look into this and understand it. Money Saving Expert site has some calculators. Uni is another reason it is a good idea for your kids to get a job. National chains will often help students transfer their job to university city. Job experience will help them with future work. Decide what chunk you are going to set aside to help with uni (don't give it to the kids - it is a float e.g. for property bonds, paying rent while waiting for loan etc) e.g. 2k each.
I would set aside a chunk for a 3k holiday each year for the next 5 years. 3k x 5 = 15k.
It is important what the giver intends of the 25k - why not run your ideas past them. Do they think a holiday is "wasted" money or do they want to give you the money for exactly things like that as they can see you haven't afforded holidays?
My budget idea:
3k holiday for next 5 years = £15k
2k each cars pot =4k
2k each uni pot = £4k
2k left added to emergency fund.
No more CTF payments, no unneccessary overpaying. Put some responsibilty onto teens to earn towards their spends and to moderate their spending.
With the cost of living increases you are going to have to budget hard if you don't want the money to leak away on bills.
Good luck. Nice problem to have! (how to spend 25k)