There is no scientific evidence to support the safety or efficacy of giving MMR vaccination as three separate vaccines at defined intervals. Using separate vaccines would lessen the take-up of vaccination, increasing the risk of these diseases returning. Having separate vaccines means there are delays between the jabs - leaving children at risk of infection from measles, mumps and rubella. When the single measles vaccine was in use in the UK, there were regular measles epidemics, killing between 10-20 children each year.
My kids have sometimes been irritable, tired or had a fever after an immunisation. This could be a coincidence. It could be a normal minor side effect from the injection and associated immune response. Scientists study risks and benefits of vaccinations and the evidence is conclusive that it is a major health benefit, particularly with herd immunity. If you want to read up on research results rather than anti-vax hysteria, the following is a good site that exposes much of the anti-vax pseudo science.